The Libradtran Software Package for Radiative Transfer Calculations (Version 2.0.1)

Manuscript prepared for Geosci. Model Dev. with version 5.0 of the LATEX class copernicus.cls. Date: 12 April 2016

The libRadtran software package for radiative transfer calculations (Version 2.0.1)

Claudia Emde1, Robert Buras-Schnell5, Arve Kylling2, Bernhard Mayer1, Josef Gasteiger1, Ulrich Hamann4, Jonas Kylling2,3, Bettina Richter1, Christian Pause1, Timothy Dowling6, and Luca Bugliaro7 1Meteorological Institute, Ludwig-Maximilians-University, Theresienstr. 37, D-80333 Munich, Germany 2NILU – Norwegian Institute for Air Research, Kjeller, Norway 3Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, Norway 4MeteoSwiss, Radar, Satellite and Nowcasting Division, Via ai Monti 146, Locarno, Switzerland 5Schnell Algorithms, Am Erdapfelgarten¨ 1, 82205 Gilching, Germany 6Dept. of Physics & Astronomy, University of Louisville, KY 40292 USA 7Institut fur¨ Physik der Atmosphare,¨ Deutsches Zentrum fur¨ Luft- und Raumfahrt (DLR), Oberpfaffenhofen, 82234 Wessling, Germany

Correspondence to: Claudia Emde ([email protected])

Abstract. libRadtran is a widely used software package for 25 1 Introduction radiative transfer calculations. It allows to compute (polarized) radiances, irradiances, and actinic fluxes in the so- Radiative transfer modeling is essential for remote sensing lar and thermal spectral regions. libRadtran has been used of planetary atmospheres, but also for many other fields in 5 for various applications, including remote sensing of clouds, atmospheric physics: e.g., atmospheric chemistry which is aerosols and trace gases in the Earth’s atmosphere, climate largely influenced by photochemical reactions, calculation of studies, e.g., for the calculation of radiative forcing due to 30 radiative forcing in climate models, and radiatively driven different atmospheric components, for UV-forcasting, the dynamics in numerical weather prediction models. calculation of photolysis frequencies, and for remote sens- The libRadtran software package is a versatile toolbox 10 ing of other planets in our solar system. The package has which has been used for various applications related to at- been described in Mayer and Kylling (2005). Since then sev- mospheric radiation, a list of publications that have used the eral new features have been included, for example polar- 35 package can be found on the website http://www.libradtran. ization, Raman scattering, a new molecular gas absorption org, currently it includes more than 400 entries. Applications parameterization, and several new cloud and aerosol scat- include the following topics (the given references are taken 15 tering parameterizations. Furthermore a graphical user in- as examples out of the list of publications): terface is now available which greatly simplifies the usage of the model, especially for new users. This paper gives an – Analysis of UV-radiation measurements, from which overview of libRadtran version 2.0.1 with focus on new fea- 40 parameters like e.g. ozone concentrations, aerosol opti- tures. Applications including these new features are provided cal thickness, UV-index are derived. Since the libRad- tran package originally was a radiative transfer code for 20 as examples of use. A complete description of libRadtran and all its input options is given in the user manual included in the UV spectral range (the main executable is still called the libRadtran software package, which is freely available at uvspec), the model is well established in this research http://www.libradtran.org. 45 area and frequently used (e.g. Seckmeyer et al., 2008; Kreuter et al., 2014).

– Cloud and aerosol remote sensing using measurements in solar and thermal spectral regions. The developed retrieval methods are for ground-based, satellite 2 C. Emde et al.: The libRadtran software package

50 and air-borne instruments which measure (polarized) ra- Since the publication of the first libRadtran reference pa- diances (e.g. Painemal and Zuidema, 2011; Bugliaro per (Mayer and Kylling, 2005) the model has been further et al., 2011; Zinner et al., 2010; Alexandrov et al., developed. It includes numerous new features which will be 2012). the focus of this paper. 100 One of the major extensions is the implementation of po- – Volcanic ash studies including remote sensing of ash larization in the radiative transfer solver MYSTIC (Emde 55 mass concentrations (e.g. Gasteiger et al., 2011; Kylling et al., 2010), which is important because an increasing num- et al., 2015) and visibility of ash particles from the pi- ber of polarimetric observations have been performed during lot’s perspective (e.g. Weinzierl et al., 2012). the last years and are planned for the future, from ground, 105 satellite, and aircraft. These observations include more in- – Remote sensing of surface properties; a model like formation about optical and microphysical properties of at- libRadtran is particularly important to develop atmo- mospheric particles than total radiances alone (Kokhanovsky 60 spheric correction methods (e.g. Drusch et al., 2012; et al., 2010; Mishchenko et al., 2007). Another important Schulmann et al., 2015). reason for considering polarization is that in the short-wave – Trace gas remote sensing, libRadtran can be used as 110 spectral region (below about 500 nm) the neglection of polarization can lead to large errors: more than 10% for a molecu- forward model for retrievals of O3, NO2 and BrO from DOAS (Differential Optical Absorption Spectroscopy) lar atmosphere and up to 5% for an atmosphere with aerosol 65 measurements (e.g. Theys et al., 2007; Emde et al., (Mishchenko et al., 1994; Kotchenova et al., 2006). 2011). Moreover libRadtran now includes a solver to calculate 115 rotational Raman scattering (Kylling et al., 2011) which im- – Calculation of actinic fluxes in order to quantify pho- proves the accuracy of trace gas retrievals. Further the Raman tolysis rates for atmospheric chemistry (e.g. Suminska-´ scattering signal can be used to estimate cloud top pressure Ebersoldt et al., 2012). from satellite measurements and aerosol properties from surface and satellite observations. 70 – Determination of solar direct irradiance and global ir- 120 Numerous state-of-the-art parameterizations for aerosol radiance distributions in order to optimize locations of and ice cloud optical properties have been included (see solar energy platforms (e.g. Lohmann et al., 2006) and Secs. 5 and 6). These new parameterizations provide more calculation of circumsolar irradiance (Reinhardt et al., accurate radiance calculations. In particular for polarized ra- 2014). diative transfer, which requires not only a scattering phase 125 function but the full scattering matrix, new data on optical 75 – Simulation of satellite radiances to be used for data properties were required. In order to improve the accuracy assimilation in numerical weather prediction models for highly peaked phase functions – which are typical for ice (Kostka et al., 2014). clouds – an improved intensity correction method has been – Validation of radiation schemes included in climate developed and included into the DISORT solver (Buras et al., models (Forster et al., 2011), calculation of radiative 130 2011), and new variance reduction methods have been devel- 80 forcing of clouds and contrail cirrus (Forster et al., oped for the Monte Carlo solver MYSTIC (Buras and Mayer, 2012), impacts of aviation on climate (e.g. Lee et al., 2011). libRadtran has also been rewritten to allow simula- 2010) tions with an arbitrary number of cloud and aerosol types – which can e.g. be used to take into account detailed particle – Simulation of heating rates in three-dimensional atmo- 135 size distributions (number densities for discretized size bins) spheres to develop fast radiation parameterizations for that can be different in each layer. In earlier versions it was 85 Large Eddy Simulation (LES) models (Klinger and only possible to take into account parameterized size distri- Mayer, 2014). butions such as gamma or log-normal distributions. A new gas absorption parameterization for the solar and – total eclipse Simulation of solar radiation during a 140 thermal spectral ranges has been developed (Gasteiger et al., (Emde and Mayer, 2007). 2014). It is available in different spectral resolutions and can be applied for the simulation of radiances and irradiances. – Rotational Raman scattering, which explains the It is particularly useful for efficient simulations of radiances 90 filling-in of Fraunhofer lines in the solar spectrum measured by satellite instruments (see Sec. 4.1). (Kylling et al., 2011). 145 The DISORT radiative transfer solver has been translated – Estimation of background radiation affecting lidar from FORTRAN77 to the C programming language. All vari- measurements (e.g. Ehret et al., 2008) ables were transferred from single to double precision. These changes improved the numerical stability of the code and re- – Remote sensing of planetary atmospheres (e.g. Ran- duced computational time significantly (for details see Buras 95 nou et al., 2010) 150 et al., 2011). C. Emde et al.: The libRadtran software package 3

The paper is organized as follows: Sec. 2 provides an 175 tration profiles, ...) needs to be provided as input to the overview of the uvspec radiative transfer model which is model. the core of the libRadtran package. Sec. 3 gives a short description of the radiative transfer solvers included in uvspec. 2. The user may select between various parameteriza- 155 Sec. 4 provides a summary of how molecules are han- tions to convert the atmospheric state into optical prop- dled and outlines various ways to include molecular absorp- erties, e.g. to convert from cloud liquid water content tion. Moreover Rayleigh scattering parameterizations are de- 180 and effective droplet size to extinction coefficient, sin- scribed. Sec. 5 summarizes the available parameterizations gle scattering albedo and scattering phase function, or for aerosol microphysical and optical properties. Sec. 6 gives phase matrix when polarization is considered. 160 an overview of the parameterizations for water and ice clouds and also outlines how these were generated. In Sec. 7 avail- 3. The optical properties are passed to a radiative transfer able surface properties are described, including Lambertian equation (RTE) solver, where again it is up to the user reflection, bidirectional distribution functions and fluorescent 185 to select the most appropriate one for the given applica- surfaces. In Sec. 8 we describe code and implementation im- tion. Currently, more than a dozen different solvers are 165 provements relevant for users. Sec. 9 introduces the graphical included in uvspec. The six most used and maintained user interface for uvspec. Sec. 10 provides a short summary RTE solvers are listed in Table 1 and briefly described in of additional tools that come with the libRadtran package. Sec. 3. Among them are relatively simple and fast two- Finally Sec. 11 shows a few applications as examples of the 190 stream solvers to compute irradiances, the widely used usage of libRadtran. discrete ordinate solver DISORT and also the Monte Carlo solver MYSTIC to compute (polarized) radiances or irradiances in three-dimensional geometry. 170 2 The uvspec radiative transfer model 4. The output of the RTE solver are radiation quantities 195 as irradiance, actinic flux or (polarized) radiance. The quantities are normalized to the source function, i.e. the Atmospheric Optical properties description solar irradiance in the solar spectral region. In order to -Trace gas profiles Profiles of: get physical quantities with corresponding units the out- -Temperature profile Absorption - extinction coefficient put may be postprocessed. The uvspec output then cor- - Pressure profile cross sections, - single scattering - Aerosol parameterizatios, albedo 200 responds to calibrated radiances or brightness tempera- - Water clouds aerosol and - scattering phase tures for a given instrumental filter function. It is also - Ice clouds cloud physics, function/matrix or ... - Surface properties Legendre polynomials possible to obtain integrated solar or thermal irradiance. (albedo or BRDF) - reflectance function/ - Wind speed matrix - ... The overall structure of the uvspec model is shown in Fig. 1. The model was originally designed to compute UV- 205 radiation, therefore its name is uvspec. As said before it now Radiation quantities RTE covers the complete solar and thermal spectral range. uncalibrated radiance/Stokes vector, solver The usage of the model is described in the user guide irradiance, actinic flux which comes along with the package. The user guide includes descriptions of the RTE solvers, examples of use as Post- 210 well as detailed documentation of all options and respective processing parameters. Below uvspec input options are put in teletype- font, for example rte solver. The uvspec model may be run either from the command Model output line using - calibrated radiance/Stokes vector, irradiance, actinic flux - integrated solar or thermal irradiance 215 uvspec < input_file > output_file - brightness temperature or from the Graphical User Interface (see Sec. 9). - simulated measurements of satellite or ground based radiometers - ...

3 Radiative transfer equation solvers Fig. 1. Structure of the uvspec radiative transfer model. The RTE for a macroscopically isotropic medium, i.e. ran- The main tool of the libRadtran package is the uvspec ra- domly oriented particles and molecules, may be written as diative transfer model, which consists of the following parts: 220 (Chandrasekhar, 1950; Mishchenko et al., 2002)

1. The atmospheric state (e.g. trace gas proﬁles, cloud dI = −I + J (1) liquid water content, cloud droplet size, aerosol concen- βds 4 C. Emde et al.: The libRadtran software package

Table 1. The radiative transfer equation solvers currently implemented in libRadtran.

RTE Geometry Radiation References Method solver quantities disort 1D, PP, PS E, F, L Stamnes et al. (1988, 2000); Buras et al. (2011); discrete ordinate, C-version Dahlback and Stamnes (1991) mystic 1D, 3D(a), PP, SP E, F, L, I Mayer (2009); Emde and Mayer (2007); Emde Monte Carlo et al. (2010); Mayer et al. (2010); Buras and Mayer (2011); Emde et al. (2011); Klinger and Mayer (2014) twostr 1D, PS E, F Kylling et al. (1995) two-stream, rodents 1D, PP E Zdunkowski et al. (2007) two-stream, plane-parallel sslidar 1D, PP ∗ single scattering lidar tzs 1D, PP L(TOA) thermal, zero scattering (a) 3D version not included in the free package; available in joint projects Explanation: PP, plane-parallel E, irradiance PS, pseudo-spherical F, actinic ﬂux SP, fully spherical L, radiance 1D, one-dimensional L(TOA), radiance at top of atmosphere 3D, three-dimensional I is the Stokes vector (polarized radiance) ∗ sslidar: see section 3.4

where the source function J is location (not possible in FORTRAN77). As such, the C ver- Z sion is numerically stable and also faster than the original ω0 0 0 0 J = P(Ω,Ω )I(Ω )dΩ + (1 − ω )B (T ) (2) 250 FORTRAN77 version. We thus use the C version of the DIS- 4π 0 e ORT algorithm by default. The original FORTRAN77 ver- Here I = (I,Q,U,V ) is the Stokes vector at location sion may still be invoked by fdisort2. Both the C-code 225 (x,y,z), β the volume extinction coefficient, ω0 the single and the FORTRAN77 version include the new intensity cor- scattering albedo, P(Ω,Ω0) the scattering phase matrix, and rection method for peaked phase functions by Buras et al. Be(T ) = (B(T ),0,0,0) the emission vector including the 255 (2011), which is used by default. Planck function B(T ). For most applications in the Earth’s For calculations with rotational Raman scattering, the C atmosphere, thermal emission can be neglected for wave- version has been generalized so that arbitrary source func- 230 lengths below about 3 µm. Polarization is also often ne- tions (not only a solar or thermal source function) can be han- glected, in this case the Stokes vector in Eqs. 1 and 2 is dled (Kylling and Stamnes, 1992; Kylling et al., 2011). Ro- replaced by the radiance L, the phase matrix becomes the 260 tational (inelastic) Raman scattering from other wavelengths scalar phase function p(Ω,Ω0) and the emission vector is just into the wavelength, for which the radiative transfer equation the Planck function B(T ). is solved, is included into the source term. 235 The uvspec model includes various methods to solve Eq. 1. The list of solvers which may be selected using the option 3.2 MYSTIC rte solver is shown in Table 1. The most comprehensive solver in libRadtran is the Monte 3.1 DISORT 265 Carlo model MYSTIC (Mayer, 2009), which may be used to calculate (polarized) radiances, irradiances and actinic The solver disort is used by default in libRadtran. DIS- fluxes in the solar and thermal spectral regions. Within MYS- 240 ORT (Stamnes et al., 2000) is based on discrete ordinates and TIC photons are traced through the atmosphere from the allows to compute radiances, irradiances and actinic fluxes in source towards the sensor or backwards, from the sensor to plane-parallel geometry. The original FORTRAN77 version 270 the source, which is much more efficient especially in the of the algorithm exhibited several numerical instabilities for thermal wavelength region. One of the main applications of certain combinations of geometries and optical properties. MYSTIC is to calculate radiances in cloudy atmospheres. 245 The FORTRAN77 code has been translated to C-code and The sharp forward scattering of clouds and aerosols causes is entirely in double precision (the FORTRAN77 version is numerical problems in Monte Carlo models. In order to avoid mostly in single precision) and includes dynamic memory al- 275 these, sophisticated variance reduction methods have been C. Emde et al.: The libRadtran software package 5

developed (Buras and Mayer, 2011). These are enabled using 3.4 Lidar and radar simulations mc vroom on. Solar radiation is initially unpolarized and becomes polarized by molecular, aerosol or cloud scatter- In order to complement the instruments that can be simu- ing in the atmosphere. With the option mc polarisation lated by libRadtran, a lidar simulator called sslidar has 280 (Emde et al., 2010) the full Stokes vector is calculated. For 325 been implemented. It only takes into account single scatter- 1D atmospheres MYSTIC may also be operated in spheri- ing and reflection and is based on the lidar equation which cal geometry using the option mc spherical (Emde and is integrated over each range. Note that in order to obtain a Mayer, 2007). smooth signal, a fine vertical resolution of the model atmo- The public version of MYSTIC allows calculations in sphere is required. The vertical resolution should correspond 285 1D (plane-parallel or spherical) geometry. A full 3D ver- 330 to the range width of the simulated lidar instrument. For radar sion is also available for joint projects. The non-public ver- simulations a stand-alone tool is available (see Sec. 10.2). sion includes several other features: Complex 3D topography (Mayer et al., 2010) and efficient high spectral resolution cal- 3.5 Other solvers culations using absorption lines importance sampling (Emde 290 et al., 2011). The solver tzs (see Appendix B) is based on the zero scattering approximation in the thermal spectral range. It may be 3.3 Two-stream solvers 335 used for clear sky calculations of radiances at top of atmosphere (TOA). It also calculates “black cloud” radiances for For the calculation of irradiances, two fast two-stream the application of the CO slicing algorithm (Smith et al., solvers are available. 2 1970; Chahine, 1974; Smith and Platt, 1978; Menzel et al., The first solver, twostr, is described in detail in Kylling 1983; Eyre and Menzel, 1989) which may be used for the 295 et al. (1995). twostr is optimized for calculating actinic 340 determination of cloud top temperatures from passive remote fluxes, and hence heating rates. It can be run in plane-parallel sensing measurements in the thermal spectral range. as well as in pseudo-spherical geometry. For the solar region a fast single scattering solver sss is The second two-stream method available in libRad- available. These solvers may be used for fast but approximate tran is rodents, which is based on the delta-Eddington simulations of satellite measurements. 300 two-stream described e.g. in Zdunkowski et al. (2007), 345 Several other RTE-solvers are included in uvspec for com- Sec. 6.1–6.41. Based on a different two-stream approach than patibility with earlier releases of the package. These include twostr, it naturally yields different results. In contrast to sdisort (pseudospherical disort), spsdisort (single twostr neither the pseudo-spherical approximation is im- precision, pseudospherical disort), fdisort1 (version 1 of plemented nor is rodents capable of calculating actinic DISORT), and polradtran (Evans and Stephens, 1991). 305 fluxes. 350 While they may still be used, we do not recommend their use For actinic fluxes and atmospheric heating rates, twostr as the other solvers listed in Table 1 perform better. is the better choice. However, for calculating solar irradiances, we recommend using rodents: For cases where the resulting irradiance is not negligible (larger than 2% 3.6 Accuracy of solvers 310 of the extraterrestial irradiance), the difference between rodents and exact disort calculations is on average The MYSTIC model has been validated in many interna- 5% (7%) for down(up)-welling irradiances. For twostr the tional model intercomparison studies, for radiance calcu- values are 9% (11%). Especially in case the atmosphere is 355 lations with highly peaked phase functions (Kokhanovsky only weakly absorbing, the average differences at top-of- et al., 2010), for polarized radiance calculations (Emde et al., 315 atmosphere (TOA) and at the surface are only 2% (1%) 2015), and for radiances and irradiances in 3D model do- for rodents, whereas they are 5% at TOA and even 13% mains (Cahalan et al., 2005). In all studies MYSTIC belongs (18%) at surface for twostr. to the core of models which produce equal results within their For the thermal irradiance, rodents also gives better re- 360 uncertainty range. MYSTIC agrees perfectly to DISORT for sults at TOA (1.6%) and at the surface (1%) than twostr radiances and irradiances with only a few exceptions, e.g. 320 (3%). For irradiances within the atmosphere, no real prefer- for circum-solar radiation, where the second-order intensity ence can be given. correction included in DISORT is not accurate enough for highly peaked scattering phase functions (Buras et al., 2011). 365 In Emde et al. (2011), a comparison between DISORT and 1Note that Zdunkowski et al. (2007) contains two misprints rele- MYSTIC for a radiance spectrum in the O2A-band is shown. vant for the twostream solver: First, in Eq. 6.50, α12,Ed = −α21,Ed 2 The relative difference between the solvers is here less than and α22,Ed = −α11,Ed. Second, α2 in Eq. 6.88 should be α2. Also, the derivation in section 6.5 for thermal radiation does not work, 0.05%. All other solvers are approximations and hence less instead the equations need to be derived in analogy to the solar ra- accurate: as mentioned before the two-stream solvers are diation. 370 only appropriate for irradiances and the tzs solver only pro- 6 C. Emde et al.: The libRadtran software package

vides radiances in thermal atmospheres and neglects scatter- For the simulation of radiances and irradiances we recom- ing completely. mend to use reptran because it is faster and more accurate The accuracy of MYSTIC depends only on the number of than lowtran. traced photons. The standard deviation of MYSTIC is cal- 425 Several correlated-k parameterizations with different num- 375 culated when the option mc std is enabled. The user may bers of bands, i.e. different accuracy, are included in libRad- run MYSTIC with many photons as reference for some cases tran. For the calculation of integrated solar and thermal irra- in order to check the accuracy of other solvers for speciﬁc diances and heating rates the correlated-k parameterizations applications. by Kato et al. (1999) and Fu and Liou (1992, 1993) are rec- 430 ommended. Also for the calculation of heating/cooling rates in the higher atmosphere (above 20 km) we recommend 4 Molecules these parameterizations because reptran and lowtran are affected by large errors.

380 4.1 Molecular absorption parameterizations 4.2 Molecular absorption cross sections Spectral ranges affected by molecular absorption comprising a complex line structure require parameterizations to reduce 435 For the spectral region from 160 to 850 nm libRadtran the computational cost. Molecular absorption parameteriza- includes measured absorption cross sections of various tions included in libRadtran are listed in Table 2. By default molecules in the atmosphere (see Table 3). Using the option 385 the reptran parameterization is applied. Using the option mol abs param crs these cross sections are used instead mol abs param the user may select the most appropriate of the default reptran parameterization. For wavelengths parameterization for the specific application. As an example 440 below 500 nm reptran yields approximately the same re- Fig. 2 shows radiance calculations for nadir viewing direc- sults as mol abs param crs because the cross sections tion at the top of the atmosphere using the parameterizations from HITRAN and the continua are very small at these wave- 390 reptran and lowtran and line-by-line calculations. lengths and the same measured cross sections are relevant in The reptran parameterization (Gasteiger et al., 2014) both cases. has recently been included in libRadtran. In reptran in- 445 For O2 for instance the cross section data include the tegrals over spectral intervals, e.g. integrated over a narrow Schumann-Runge bands between 176 and 192.6 nm and the spectral band or an instrument channel response function, are Herzberg continuum between 205 and 240 nm. Ozone ab- 395 parameterized as weighted means over representative wave- sorption bands are for example the Huggins bands between lengths similar to the method described by Buehler et al. 320 and 360 nm and the Chappuis bands between 375 and (2010). The selection of an optimum set of representative 450 650 nm. Using the option crs model the user may spec- wavelengths is based on accurate line-by-line simulations for ify which cross section data should be used in the simula- top of atmosphere radiances of a highly variable set of atmo- tions. Alternatively with crs file the users may specify 400 spheric states. The ARTS model (Eriksson et al., 2011) in- their own absorption cross section data. cluding state-of-the-art continuum models and spectroscopic data from HITRAN 2004 (Rothman et al., 2005) were used 4.3 Line-by-line calculations to calculate the gas absorption properties. For wavelengths below 1130 nm measured absorption cross sections of O3 455 In the shortwave infrared, thermal infrared and microwave 405 (Molina and Molina, 1986), O4 (Greenblatt et al., 1990), region we find a huge number of absorption lines which and NO2 (Burrows et al., 1998) are included, as they are are due to vibrational or rotational transitions in molecules. not covered by HITRAN or the continua (see also Sec. 4.2). A line-by-line model is required in order to calculate spec- Three band resolutions (fine: 1 cm−1, medium: 5 cm−1 , and trally resolved radiances. Line-by-line models take the ab- −1 coarse: 15 cm ) are available in the solar and thermal spec- 460 sorption line positions as well as line strength parameters 410 tral range, as well as a number of instrument channels on the from spectral databases like HITRAN, calculate line broad- ADEOS, ALOS, EarthCARE, Envisat, ERS, Landsat, MSG, ening which depends on pressure and temperature in the at- PARASOL, Proba, Sentinel, Seosat, and SPOT satellites. The mosphere and finally obtain absorption optical thickness pro- parameterization has been validated by comparison to high files. libRadtran does not include a line-by-line model but spectral resolution calculations. For solar and thermal radia- 465 it allows to specify absorption optical thickness profiles us- 415 tion at the top of atmosphere, as well as for solar radiation at ing the option mol tau file abs. It is convenient to use the ground, the mean parameterization error is in the range the ARTS model (Eriksson et al., 2011) to generate spec- of 1%. The mean error is slightly larger than 1% for thermal trally resolved molecular absorption data because it outputs radiation at the surface. the format required by libRadtran. ARTS includes a compre- The LOWTRAN band model adopted from from the SB- 470 hensive line-by-line module, it allows to use different spec- 420 DART radiative transfer model (Ricchiazzi et al., 1998) is troscopic databases like HITRAN as input and it also in- also included in libRadtran. cludes various state-of-the-art absorption continuum models. C. Emde et al.: The libRadtran software package 7

0.06 300

290 0.05 280 0.04 270

0.03 260

250 0.02 240 normalized radiance 0.01

brightness temperature [K] 230

0.00 220 755 760 765 770 775 9000 9500 10000 10500 11000

0.06 300

0.05 290

0.04 280

0.03 270 reptran fine 0.02 260 reptran medium normalized radiance 0.01 250 reptran coarse brightness temperature [K] lowtran 0.00 240 755 760 765 770 775 9000 9500 10000 10500 11000 wavelength [nm] wavelength [nm]

Fig. 2. Nadir top of the atmosphere radiance in the oxygen-A band around 760 nm (left) and in the IR window region (right) for the midlatitude-summer atmosphere of Anderson et al. (1986). All calculations were performed with the MYSTIC solver using the “absorption lines importance sampling” method (Emde et al., 2011). (Top) High spectral resolution calculation, based on line-by-line absorption cross sections calculated using ARTS (Eriksson et al., 2011); (bottom) pseudo-spectral calculations using the representative wavelengths band parameterizations (reptran) with different resolutions and lowtran. For comparison see also Fig. 3 in Mayer and Kylling (2005) which shows transmittances for genln2 line-by-line calculations and lowtran for the same spectral regions.

Table 2. Absorption parameterizations in libRadtran.

Name Description Application References reptran default setting; calculation of radiances, Gasteiger et al. (2014) bands parameterized using repr. wavelengths; simulation of satellite measure- ﬁne (1cm−1), medium (5cm−1) and coarse ments (15cm−1) band resolutions available; based on HITRAN2004, MT CKD and measured absorption cross section data of O3,O4, and NO2; solar and thermal region reptran channel satellite channels parameterized using fast and accurate simulations Gasteiger et al. (2014) representative wavelengths; for various satellite instruments lowtran LOWTRAN band model; pseudo-spectral calculations of Ricchiazzi et al. (1998) solar and thermal region, resolution 20 cm−1 radiances Pierluissi and Peng (1985) kato, kato2 correlated k distributions for solar region; calculation of integrated solar Kato et al. (1999) kato2.96, different versions available; irradiance Wandji Nyamsi et al. (2015) katoandwandji based on HITRAN96 or HITRAN2000; 148 or 575 sub-bands fu correlated k distributions for solar (6 bands) calculation of integrated solar Fu and Liou (1992, 1993) and thermal (12 bands) regions; and thermal irradiance, optimized for climate models radiative forcing 8 C. Emde et al.: The libRadtran software package

Table 3. Absorption cross section data included in libRadtran, the where non-default parameterizations are put in parantheses. 1 − δ 0 1 − 2δ 490 ∆ = , ∆ = , (3) 1 + δ/2 1 − δ

Molecule wavelength range [nm] reference and δ is the depolarization factor that accounts for the anisotropy of the molecules, δ is also calculated according to BrO 312 – 385 Wahner et al. (1988) Bodhaine et al. (1999). The Rayleigh phase matrix for δ=0 is CO2 119 – 200 Yoshino et al. (1996) shown in Fig 3. For calculations neglecting polarization only HCHO 300 – 386 Cantrell et al. (1990) 495 the (1,1) element of the phase matrix which corresponds to NO2 240 – 760 (Bogumil et al. (2003)) 231 – 794 Burrows et al. (1998) the scattering phase function is required. O2 108 – 160 Ogawa and Ogawa (1975) 160 – 175 Yoshino et al. (2005) 5 Aerosols 175 – 204 Minschwaner et al. (1992) 205 – 240 Yoshino et al. (1988) Besides the models by Shettle (1989) which are described O 116 – 185 Ackerman (1971) 3 in Mayer and Kylling (2005), libRadtran now includes ad- 185 – 350 Molina and Molina (1986) 195 – 345 (Daumont et al. (1992))/ 500 ditional aerosol properties based on the OPAC database (Malicet et al. (1995)) (Hess et al., 1998). OPAC provides the required parame- 245 – 340 (Bass and Paur (1985)) ters for single scattering calculations: size distribution pa- 240 – 850 (Bogumil et al. (2003)) rameters, refractive indices, and the density of the mate- 400 – 850 WMO (1986) rial. Data are available for the spectral range from 250 nm O4 330 – 1130 Greenblatt et al. (1990) 505 to 40 µm for the following basic aerosol types: insoluble OClO 240 – 480 Wahner et al. (1987) (inso), water soluble (waso), soot (soot), sea salt accu- SO2 239 – 395 Bogumil et al. (2003) mulated (ssam), sea salt coarse mode (sscm), mineral nu- cleation mode (minm), mineral accumulated mode (miam), mineral coarse mode (micm), mineral transported (mitr) The toolbox Py4CATS (Schreier and Bottger,¨ 2003; Schreier, 510 and soluble sulfate aerosol (suso). For the soluble aerosols 2006; Schreier and Kohlert, 2008) which can be downloaded the parameters depend on humidity because the aerosol par- 475 from www.libradtran.org also includes convenient command ticles swell in humid air. Relative humidities of 0%, 50%, line programs to generate spectrally resolved absorption data. 70%, 80%, 90%, 95%, 98% and 99% are included in OPAC. The Py4CATS tools however do not include continuum mod- The option aerosol species file allows to define ar- els, hence it should only be used for simulations where the 515 bitrary mixtures of these basic types or to select pre-defined continua are not relevant. mixtures from OPAC like e.g. continental average, for which uvspec automatically uses the optical properties 480 4.4 Rayleigh scattering cross sections closest to the background humidity profile. Optical properties of all basic aerosol types were calcu- The Rayleigh scattering cross sections are by default calcu- 520 lated using libRadtran’s Mie tool (see Sec. 10.1). For mineral lated using Eqs. 22–23 of Bodhaine et al. (1999). Using the aerosols, which are highly aspherical, we additionally pro- option crs model rayleigh the user may select Eq. 29 vide optical properties calculated with the T-matrix method of Bodhaine et al. (1999) or the formulas proposed by Nico- (Mishchenko and Travis, 1998) assuming an aspect ratio dis- 485 let (1984) and Penndorf (1957), respectively. The analytical tribution of prolate spheroids as described by Koepke et al. P Rayleigh scattering phase matrix R (Hansen and Travis, 525 (2015). 1974) is As an example Fig. 3 shows the phase matrix elements of the basic OPAC aerosol types, of liquid cloud droplets with an effective radius of 10 µm and the Rayleigh scat-

PR(Θ) = tering phase matrix. Note that for spherical particles only 530 4 elements of the 4x4 scattering phase matrix are indepen-  3 2 3 2  4 (1 + cos Θ) − 4 sin Θ 0 0 dent whereas for aspherical particles 6 elements are required 3 2 3 2  − 4 sin Θ 4 (1 + cos Θ) 0 0  (see e.g. Hansen and Travis, 1974). Fig. 4 shows the absorp- ∆ 3   0 0 2 cosΘ 0  tion and the scattering optical thicknesses (integrated from 0 3 0 0 0 ∆ 2 cosΘ the surface to the top of the atmosphere) for the standard   535 aerosol mixtures in the spectral region from 300 to 800 nm. 1 0 0 0 As expected, the optical thickness of the urban aerosol is  0 0 0 0  +(1 − ∆) , the largest and that of the antarctic aerosol the smallest.  0 0 0 0  In general the continental aerosol mixtures show a stronger 0 0 0 0 wavelength dependency than the maritime mixtures. C. Emde et al.: The libRadtran software package 9

540 The users may also provide their own optical properties data which may be generated using libRadtran’s Mie tool or other external programs; more detailed instructions are pro- P11 = P22 P12/P11 104 0.4 vided in the libRadtran user guide. Rayleigh 103 0.2 waso 95% RH 0.0 102 ssam 95% RH 0.2 6 Clouds soot − 101 cloud 10µm 0.4 − 545 100 6.1 Water clouds 0.6 − 1 10− 0.8 − Table 4 summarizes the parameterizations of water cloud op- 10 2 1.0 − 0 20 40 60 80 100 120 140 160 180 − 0 20 40 60 80 100 120 140 160 180 tical properties which may be selected in libRadtran using P33/P11 P34/P11 the option wc properties. 1.5 0.8 For the simulation of irradiances and heating rates it is 1.0 0.6 550 normally sufﬁcient to use a simple parameterization to con- 0.5 0.4 vert from cloud liquid water content and droplet effective

0.0 0.2 radius to the respective optical properties: extinction coefficient, single scattering albedo, and asymmetry parameter. For 0.5 0.0 − this purpose libRadtran includes the parameterization gener- 1.0 0.2 − − 555 ated by Hu and Stamnes (1993). 1.5 0.4 − 0 20 40 60 80 100 120 140 160 180 − 0 20 40 60 80 100 120 140 160 180 For the simulation of radiances more accurate optical θ [ deg ] θ [ deg ] properties are needed and the phase function should not be approximated by a Henyey-Greenstein function as it is done Fig. 3. Phase matrix elements for the basic OPAC aerosol types in Hu and Stamnes (1993). Therefore, we have pre-calculated “water soluble” (waso), “sea salt accumulated mode” (ssam), and 560 cloud optical properties using libRadtran’s Mie tool assum- soot, for a water cloud with a droplet effective radius of 10 µm, ing that the cloud droplets are gamma distributed: and for Rayleigh scattering (with δ=0) at a wavelength of 350 nm. θ is the scattering angle, i.e. the angle between incoming and scattered r 1 n(r) = Nrα exp − ; α = − 3 (4) directions. reff · veff veff

Calculations have been performed for effective radii reff from 1µm to 25µm with a step width of 1µm. The effec- 565 tive variance was set to a value of veff = 0.1 and the constant N was determined by normalization. The size distributions were cut off at a minimum radius of 0.02·r and a maximum 0.9 0.25 eff 0.8 radius of 8·reff . The size distribution bins are sampled on a 2πr 0.7 0.20 size parameter ( λ ) grid with a resolution of 0.003. This 0.6 570 fine resolution is necessary to obtain smooth phase matrices. 0.15 0.5 The pre-calculated data includes the wavelength ranges from 0.4 0.10 250 nm to 2200 nm (solar) with a resolution of 10 nm and the 0.3 range from 2.2 µm to 100 µm (thermal) in 100 steps of equal 0.2 0.05 wavenumbers. The refractive index of water has been taken

0.1 scattering optical thickness absorption optical thickness 575 0.0 0.00 from Warren (1984). In the solar (thermal) region the phase 300 400 500 600 700 800 300 400 500 600 700 800 matrices are computed from 5000 (500) Legendre polynomi- wavelength [nm] wavelength [nm] aerosol mixture name als. In the optical properties files 129 of the Legendre polyno- continental_clean maritime_clean urban mials are stored, as well as the phase matrix elements, which continental_average maritime_polluted desert are stored on scattering angle grids θ optimized such that continental_polluted maritime_tropical antarctic 580 the error of the phase matrix – when interpolated linearly in cosθ between the grid points – is smaller than 1%. As an Fig. 4. Absorption (left) and scattering (right) optical thick- example Fig. 3 shows the four phase matrix elements of a ness for various aerosol mixtures specified using the option cloud droplet distribution with reff =10 µm at 350 nm. Here ◦ aerosol species file. The aerosol optical properties as well the cloudbow at θ ≈140 is clearly visible in the P11 and as the mixtures have been generated based on OPAC (Hess et al., 585 P12/P11 elements of the phase matrix. P12/P11 corresponds 1998) parameters. to the degree of polarization in the principal plane after single scattering, it can be seen that the maximum in the cloudbow region is about 80%. The mystic solver uses the phase ma- 10 C. Emde et al.: The libRadtran software package

Table 4. Water clouds parameterizations in libRadtran.

Name Description Application References hu Default setting. Simple parameterization, uses Irradiances, heating rates Hu and Stamnes (1993) Henyey-Greenstein phase function to approximate Mie phase function echam4 Very simple two-band parameterization of Comparison of irradiances to Roeckner et al. (1996) ECHAM4 climate model results from ECHAM4 mie Optical properties calculated using Mie theory, (Polarized) radiances generated using Mie code by include full phase matrices Wiscombe (1980)

trix stored on the θ-grid, whereas all other solvers use the for rough ice crystals, and the single habits solid-column and 590 Legendre polynomials, except for the intensity correction in aggregate, both of them severely roughened. disort which uses the phase function (see also Buras et al., 630 We have generated two further parameterizations (hey 2011). and yang2013) for individual habits which also include the For specific applications, e.g. different size distributions, full phase matrices (see Appendix A): hey is available for the user can easily generate optical properties using libRad- the wavelength region from 0.2 to 5 µm for smooth parti- 595 tran’s Mie tool. cles in the effective radius range from 5 to 90 µm. The full 635 wavelength region from 200 nm to 99 µm is available for 6.2 Ice Clouds yang2013, effective radii may be in the range from 5 to 90 µm and a roughness parameter may also be specified, For ice clouds libRadtran includes a variety of parameteriza- ranging from smooth to severely rough. For the yang2013 tions (see Table 5) from which the user may select the most parameterization, the single scattering properties of nine in- appropriate one for a specific application by specifying the 640 dividual ice crystal habits which are commonly observed in 600 option ic properties. Ice clouds are more complex than ice clouds have been taken from the database by Yang et al. water clouds because they consist of ice crystals of different (2013). The hey parameterization was generated before this shapes. Some of the ice cloud parameterizations allow the database existed and it is based on single scattering data pro- crystal habit (ic habit) to be specified. vided by Hong Gang who used the improved geometrical op- As described in the previous section the exact phase matrix 645 tics method (IGOM), the same method as used by Yang et al. 605 is not needed when irradiances are calculated. For this pur- (2013). pose the parameterizations by Fu (1996); Fu et al. (1998) and Please refer to the libRadtran user guide for a list of avail- Key et al. (2002) are included in libRadtran. Fu (1996) and able habits for each parameterization. Fu et al. (1998) approximate the phase function by a Henyey- Fig. 5 shows the phase matrix elements of ice crystal dis- Greenstein function. Key et al. (2002) is slightly more ac- 650 tributions with an effective radius of 40 µm at 550 nm wave- 610 curate because it uses a double-Henyey-Greenstein function length. The red lines correspond to smooth crystals and the which represents the backscattering of ice crystals much bet- blue lines to severely rough crystals. The individual habits ter. The parameterization is based on single scattering cal- are for the yang2013 parameterization. General habit mix- culations for various ice crystal habits and on measured size tures which are available for the hey parameterization based distributions. It is available in the wavelength range from 0.2 655 on smooth crystals and for the baum v36 parameterization 615 to 5 µm. Based on single scattering data provided by P. Yang based on severely rough crystals are also shown. For most and on the size distributions from J. R. Key we have extended smooth crystals and also for the general habit mixture ghm the original parameterization by Key et al. (2002) to the ther- of the hey parameterization scattering features of hexagonal mal wavelength region up to 100 µm. ice crystals, the most prominent being the halo at 22◦ scatter- For accurate radiance calculations the parameterizations 660 ing angle, are visible in all phase matrix elements. The phase 620 by Baum et al. (2005a,b) (baum) and the newer one by matrices for severely rough crystals do not show halo fea- Heymsfield et al. (2013); Yang et al. (2013) and Baum et al. tures and they are relatively similar for all habits. In reality (2014) (baum v36) are available: baum includes full phase ice clouds are highly variable: There are situations when the functions for a mixture of particle shapes, the parameteri- halo is visible, in this case obviously there must be regular zation is based on single scattering properties of smooth ice 665 smooth ice crystals in the cirrus clouds. When no halo is vis- 625 crystals and on a large number of measured size distributions. ible, the assumption of severely roughened crystals might be baum v36 includes full phase matrices and three different more realistic. habit models: a general habit mixture similar to baum but C. Emde et al.: The libRadtran software package 11

Table 5. Ice cloud parameterizations in libRadtran

Name Description Application References fu Default setting. Simple parameterization using Irradiances, heating rates Fu (1996); Fu et al. (1998) Henyey-Greenstein phase function. echam4 Very simple 2-band parameterization of Comparison of irradiances to Roeckner et al. (1996) ECHAM4 climate model. results from ECHAM4 key Parameterization using a double-Henyey- Irradiances, heating rates Key et al. (2002) Greenstein phase function, covers wavelength range from 0.2 µm to 5.0 µm. Available for various habits. yang Similar to key but based on different single Irradiances, heating rates Key et al. (2002), Yang et al. scattering calculations and extended to wave- (2005) lengths up to 100 µm. Below 3.4 µm equivalent to key. baum Bulk optical properties including phase func- Radiances Baum et al. (2005a,b) tions for a realistic mixture of habits. Covers wavelength range from 0.4 to 2.2 µm and from 3.1 to 100 µm. baum v36 Bulk optical properties including phase ma- (Polarized) radiances Heymsﬁeld et al. (2013); Yang trices for three microphysical models: general et al. (2013); Baum et al. (2014) habit mixture, solid columns or rough aggre- gates. All models include severely rough particles. Covers wavelength range from 0.2 to 99 µm. hey Bulk optical properties including phase matri- (Polarized) radiances Single scattering properties ces based on single scattering calculations for generated by Hong Gang using smooth crystals, covers wavelength range from the code by Yang et al. (2013), 0.2 to 5 µm, includes 6 habits and a habit mix- Appendix A ture. yang2013 Bulk optical properties including phase matri- (Polarized) radiances Yang et al. (2013), Appendix A ces for 9 habits and 3 degrees of roughness, covers wavelength range from 0.2 to 99 µm.

7 Surface nel combinations, of which the RossThickLiSparseRecipro- cal combination was identified in several studies to be the 7.1 Bidirectional reflectance distribution functions 685 model best suited for the operational MODIS BRDF/Albedo algorithm (see Schaaf et al., 2002). An additional factor for simulating the hot spot in vegetation canopies was added by 670 All solvers included in libRadtran may include Lambertian surfaces, while disort and MYSTIC can also handle bidirec- Maignan et al. (2004). The version implemented in libRad- tional reflectance distribution functions. libRadtran provides tran is the RossThickLiSparseReciprocal model as used in a variety of BRDFs, which are listed in table 6. 690 MODIS data, as presented in Lucht et al. (2000). The hot Two parameterizations for land surfaces are available. spot correction factor can be turned on on demand. As already stated in Mayer and Kylling (2005), but re- 675 The first is the “RPV” parameterization by Rahman et al. (1993) with the extension by Degunther¨ and Meerkotter¨ peated here for completeness, a parameterization of the (2000) for modelling snow-covered surfaces. The second is BRDF of water surfaces is also included which depends the “RossLi” BRDF first presented by Roujean et al. (1992). 695 mainly on wind speed and to a lesser degree on plankton The original RossLi BRDF is used in the AMBRALS (the concentration and salinity. For the MYSTIC solver, also the wind direction can be set. In contrast to vegetation where 680 Algorithm for Modeling[MODIS] Bidirectional Reflectance ◦ Anisotropies of the Land Surface) BRDF Modeling Frame- the typical hot spot occurs in the 180 backscatter direction, work (Wanner et al., 1997), and consists of four different ker- the main feature for water is specular reflection. The param- 12 C. Emde et al.: The libRadtran software package

Table 6. The surface reﬂection models currently implemented in libRadtran.

Option name BRDF type # of parameters References Solvers albedo Lambertian 1 All brdf cam Ocean BRDF 3+1 Cox and Munk (1954a,b); Nakajima and Tanaka (1983) D,M bpdf tsang Polarized ocean BRDF 1 Tsang et al. (1985); Mishchenko and Travis (1997) M brdf hapke Planetary & lunar surfaces 3 Hapke (1993) D,M brdf ambrals Ross-Li, MODIS Land Surface, 3 Roujean et al. (1992); Wanner et al. (1997); Lucht et al. D,M RTLSR (2000); Schaaf et al. (2002); Maignan et al. (2004) brdf rpv Land surfaces 3+3 Rahman et al. (1993); Degunther¨ and Meerkotter¨ (2000) D,M Explanation: D: DISORT M: MYSTIC RTLSR: RossThickLiSparseReciprocal model, optionally with hot spot parameterization

700 eterization in uvspec was adopted from the 6S code (Ver- mote et al., 1997) and is based on the measurements of Cox and Munk (1954a,b) and the calculations of Nakajima and Tanaka (1983). A vector version of the ocean parameterization, developed by Tsang et al. (1985) and Mishchenko and 107 0.5 106 0.4 705 Travis (1997), is available for polarization calculations with 105 0.3 104 0.2 MYSTIC. The vector version uses only wind speed as a pa- 103 0.1 2 rameter and does not take into account plankton concentra- P11 10 0.0 1 10 P12/P11 0.1 tion, salinity or wind direction. 100 0.2 10-1 0.3 Finally, the parameterization of the surfaces of extrater- 10-2 0.4 0 30 60 90 120 150 180 0 30 60 90 120 150 180 710 restrial solid bodies such as the moon, asteroids or the inner 1.0 0.3 0.8 0.2 planets by Hapke (1993) is available. 0.6 0.4 0.1 Only the ocean BRDF parameterizations depend directly 0.2 0.0 0.0 on the wavelength. For all other BRDF models, the pa-

P33/P11 0.2 P34/P11 0.1 0.4 rameterization can either be given as being constant with 0.2 0.6 0.8 0.3 715 wavelength (by using e.g. the option brdf rpv), or as a 0 30 60 90 120 150 180 0 30 60 90 120 150 180 1.0 1.0 ﬁle containing the parameters for each wavelength (using 0.8 0.8 brdf rpv file 0.6 e.g. ). 0.6 0.4 0.2 0.4 0.0

P22/P11 0.2 P44/P11 0.2 7.2 Fluorescence 0.4 0.0 0.6 0.2 0.8 0 30 60 90 120 150 180 0 30 60 90 120 150 180 For vegetation covered surfaces, a weak solar-induced scattering angle [degrees] scattering angle [degrees] 720 chlorophyll ﬂuorescence signal is emitted in the red and far- Ice crystal habit solid_column (smooth) solid_column (sev. rough) red spectral regions. The contribution of ﬂuorescence to the column_8elements (smooth) column_8elements (sev. rough) radiance leaving the bottom boundary is plate (smooth) plate (sev. rough) HEY ghm baum_v36 ghm

F Lg (µ,φ,λ) = F (λ), (5) Fig. 5. Phase matrix elements of ice crystal distributions with an effective radius of 40 µm at 550 nm wavelength. The red lines correspond to smooth and the blue lines to severely rough where F (λ) is the fluorescence source in the same units as crystals, respectively. The individual habits (solid-column, 725 the incoming solar flux at the top of the atmosphere (for ex- column-8elements and plate) are for the parameterization ample mW/(m2 nm sr)). The fluorescence source of radiation yang2013, and the general habit mixtures (ghm) are for hey in- is included in the disort solver. It may either be constant cluding smooth crystals and baum v36 including severely rough or vary as a function of wavelength. Additional surface bidi- particles. rectional reflection of radiation may also be included. The 730 flourescence source depends on the solar radiation impinging the vegetation and the type of vegetation. Output from vegetation fluorescence canopy models such as that described by Miller et al. (2005), may readily be used by uvspec. C. Emde et al.: The libRadtran software package 13

8 Implementation improvements options that are set by the user and that will be written to the given input files are shown in bold face (for example option 735 8.1 Multiple atmospheric constituents 785 rte solver in Fig. 6). Options that may be set are shown as normal characters, while options that are not compati- The previous versions of libRadtran were restricted to using ble with other set options are greyed (for example in Fig. 6 at most four types of atmospheric constituents: molecules, mc ipa is greyed since it is not possible to combine it with aerosols, and water and ice clouds. Any user defined con- rte solver set to disort). stituent could only be included by replacing e.g. water clouds 790 On-line documentation of the options are available and 740 with them. Also, it was not possible to use several types of this is identical to the documentation in the libRadtran ice cloud habits at the same time. user manual. In Fig. 6 the documentation for the option A recent major internal restructuring of the libRadtran number of streams is shown in the lower left corner. code has now made it possible to use any number of The on-line help is activated by pointing the mouse at the atmospheric constituents for a radiative transfer simula- 795 requested input variable. 745 tion. The number is only limited by computational mem- Input options that refer to input data files, such as wave- ory and time. The new input options needed for load- length dependent surface albedo, may be plotted from the ing the additional constituents are profile file and GUI. In the example in Fig. 6, the extraterrestrial flux (up- profile properties. They work very similar to the per left subplot), the surface fluorescence spectrum (lower cloud input options; merely the name of the constituent needs 800 left subplot) and surface albedo (lower right subplot) inputs 750 to be defined. are plotted. Note that the wavelength coverage (x-axis) dif- This option increases the flexibility of libRadtran in many fers reflecting the different wavelength regions included in ways. E.g. it can be used to load the optical properties for the input data files. each size bin of an aerosol or water or ice cloud. This way, the Once all wanted input options are set, they are saved to a size distribution may differ between the atmospheric layers. 805 user specified file, and uvspec is run from within the GUI. 755 An example can be found in Kylling et al. (2013). The output from the run may readily be plotted using the GUI. For example, in Fig. 6, the calculated nadir radiance at 8.2 Change of nomenclature and backward compatibil- the top of the atmosphere is shown in the upper right subplot. ity The GUI includes numerous working examples. Users may As the number of input options had grown to more than 300 810 add more examples to the GUI specific to their interests. over the years, we decided to restructure the language of the 760 input options. The input options now have a largely consis- 10 Other tools tent naming and their usage follows certain rules, making it more easy to find related input options. Several additional tools are included in the libRadtran pack- We have included a python script in order to provide age. An overview is given in Mayer and Kylling (2005, Tab. backward compatibility for long-established libRadtran 4). New tools are ssradar, a single scattering Radar simulator 765 users. The script can be found in the directory src py. By 815 (see below), and pmom, which calculates Legendre polyno- invoking the command mials for a given phase function. python translate.py input_file \ > new_input_file 10.1 Mie calculations input files written in the old nomenclature will be translated 770 to the new nomenclature automatically. Alternatively, the old The tool for Mie calculations (mie) has been extended con- input file can be sent directly to uvspec with the following siderably. The user may select between two Mie codes, command: 820 MIEV0 by Wiscombe (1980) or bhmie by Bohren and Huff- python translate.py input_file | uvspec man (1983). The tool allows to generate input optical properties for uvspec calculations for arbitrary size distributions. It

775 generates full phase matrices which are stored on optimized angular grids for a user-deﬁned accuracy. The radiative trans- 825 fer solvers MYSTIC and DISORT with the new intensity 9 Graphical User Interface correction method (Buras et al., 2011) use the phase functions/matrices rather than Legendre polynomials, which are The large number of input options available in the uvspec calculated by the Mie codes. model may appear overwhelming. To help the user to create uvspec input ﬁles a graphical user interface (GUI) has been 10.2 Single scattering Radar simulator 780 developed. The GUI organizes the input options in logical groups such as “Molecular Atmosphere”, “Aerosol”, “Sur- 830 Single scattering Radar (ssradar) is a stand-alone 1D pure face” etc., see also the grey bar at the top in Fig. 6. Input Rayleigh-scattering cloud radar simulator that handles arbi- 14 C. Emde et al.: The libRadtran software package

Fig. 6. Screenshot of the Graphical User Interface for a spectral high-resolution simulation of the O2-B band including a ﬂuorescence source. Plots of input and output data are included together with the help information for one option. See text for further explanation.

trary cloud layers and droplet size distributions as well as with uvspec to perform line-by-line calculations in both the tilted viewing angles and supercooled water droplets. The solar and thermal parts of the spectrum. For both examples radar reflectivity factor is calculated directly from the droplet the spectral resolution, the molecules to be included and the P 6 835 distribution with Z = i niDi (Rinehart, 2010) where D is 855 line function properties are specified in the input to ARTS. It the droplet diameter and ni the distribution number density is noted that the same ambient atmospheric profile should be for the discrete interval Di,Di+1. Internally available distri- used in both, ARTS and uvspec. butions are gamma and lognormal, arbitrary distributions can be entered using input files. 11.1.1 Solar source

Solar induced chlorophyll fluorescence is emitted in the 660 840 11 Some applications 860 to 800 nm spectral region with two broad peaks at about 685 The libRadtran package has been used for numerous appli- and 740 nm. In this spectral region are the O2-A and O2- cations. Many of these are listed under the publications link B bands which contain a large number of absorption lines. at http://www.libradtran.org. The examples directory also Although the fluorescence signal is weak, especially the O2- includes a number input files that may be used especially by B region holds promise for retrieval of vegetation fluores- 865 cence from spectrally high resolution space borne instru- 845 new users to create input files. Below some applications of libRadtran are described. ments (Guanter et al., 2010). In this spectral region the surface albedo is typically low while there is a fluorescence peak 11.1 uvspec and ARTS around 685 nm (see red line lower plot Fig. 7). The optical depths from ARTS are input to uvspec which calculates The high number of absorption lines in the shortwave in- 870 the top of the atmosphere radiance (blue line, upper plot of frared and the thermal infrared requires a line-by-line ap- Fig. 7) including the fluorescence signal (red line, lower plot 850 proach to resolve the spectral structure. Below is shown how of Fig. 7), surface albedo (green line, lower plot of Fig. 7) and molecular absorption data from ARTS may be combined molecular scattering . Measurements may be made at a lower C. Emde et al.: The libRadtran software package 15

890 also be used to detect volcanic ash (see Clarisse et al., 2013, 1e13 1.0 and references therein). 1.0 The left panel of Fig. 8 shows IASI spectra from a granule ]

) Transmittance r 0.8 covering the ash cloud following the eruption of Mt. Kelud, s 0.8 Radiance 2 Indonesia, in February, 2014. The spectra are classiﬁed as m c 895 cloudless (green), ice cloud (blue), and volcanic ash (red). To

m 0.6 0.6 n investigate the realism of this identiﬁcation the spectra were s ( /

s simulated with ARTS/uvspec. For all simulated spectra, the n 0.4 o 0.4 t Transmittance

o surface emissivity was set equal to one which is representa- h p [

tive for water. The simulated spectra are shown in the right L 0.2 0.2 900 plot of Fig. 8. The cloudless spectrum has brightness temperatures rep- 0.0 0.0 675 680 685 690 695 700 resentative for the ocean at these latitudes. The main molec- Wavelength [nm] ular absorption features in this part of the spectrum are water 1e13 0.2 vapor lines throughout the spectrum, ozone (broad band fea- With fluorescence 1.0 −1 Without fluorescence 905 ture centered around 1050 cm ), and CO2 (feature below

] −1 )

r Fluorescence source (*20) 800 cm ). The data from ARTS include absorption lines s

2 Albedo 0.8 from these molecules. In the cloudless spectrum the ozone m

c −1 band around 1050 cm has a lower brigthness temperature m n than the radiation at lower and higher wavenumber, indi-

s 0.1 ( / 0.6 Albedo s 910 cating that the radiation in the ozone band was emitted at n o t

o a higher altitude with lower temperature than the surface. h p [

0.4 Overall the ARTS/uvspec cloudless spectrum agrees well L with the measured spectrum. For the simulation with an ice cloud, the ice cloud was lo- 0.2 0.0 675 680 685 690 695 700 915 cated between 12 and 13 km. Ice water content was set to Wavelength [nm] 1 g/m3. The ice particles were assumed to consist of solid columns with reff =40.0 µm. The ice cloud parameterization Fig. 7. (Upper plot) The transmittance from ARTS output and ra- ic properties yang was selected. The spectrum iden- diance from uvspec. (Lower plot) The top of the atmosphere nadir tified as ice cloud (blue curve in left plot of Fig. 8) appears viewing radiance in the O2-B band with (black line) and without 920 saturated for nearly all wavenumbers except for the ozone (cyan line with circles) a surface fluorescence source (red line with band centered around 1050 cm−1. The rather low brightness triangles). The radiances have been convolved with a spectral re- temperature and wavenumber independent behaviour outside sponse function with FWHM of 0.3 nm. the ozone band, indicates that this is an ice cloud and that it is opaque. The simulation with an ice cloud (blue curve in 925 right plot of Fig. 8) agrees well with the measured spectrum. The higher temperatures in the ozone band implies that this spectral resolution. The lower plot of Fig. 7 shows radiance radiation was emitted at a higher altitude in the stratosphere 875 spectra convolved with a triangular spectral response func- where the temperature is higher than at the altitude of the tion with a full width at half maximum (FWHM) of 0.3 nm cloud. using the conv tool of libRadtran. The spectral response func- 930 The ash simulation included an ash cloud between 17 and tion was generated with the make slitfunction tool. Spectra 18 km. The ash particles were assumed to be made of an- with (blue line) and without (purple line) fluorescence are desite, spherical and mono-disperse with a radius of 3 µm. 880 presented. It is seen that the fluorescence signal is relatively The refractive index of andesite was taken from Pollack et al. larger when the surface albedo is low, below about 690 nm, (1973) and the optical properties were calculated using the compared to larger wavelengths. −3 3 935 mie tool. The ash density was 1×10 g/m which corresponds to a mass loading of 1 g/m2 for a 1 km thick cloud. 11.1.2 Thermal source The red curve in the left plot of Fig. 8 is classified as ash using the difference in brightness temperature method de- The Infrared Atmospheric Sounding Interferometer (IASI) scribed by Clarisse et al. (2010). This spectrum has a lower 885 on board the MetOp satellite measures the radiance from 645 940 brigthness temperature than the cloudless spectrum indicat- to 2760 cm−1 (15.50-3.6 µm) with a spectral resolution of ing a colder effective emitting temperature overall. The gen- 0.25cm −1. Its main purpose is high-resolution atmospheric eral spectral shape is similar to the cloudless spectrum below sounding of temperature and humidity, and trace gas column 1000 cm−1. Above about 1200 cm−1 the brightness temper- retrievals (Clerbaux et al., 2009; Hilton et al., 2011). It may ature of the cloudless spectrum generally decreases with in- 16 C. Emde et al.: The libRadtran software package

Measured (IASI) Simulated (ARTS/uvspec) Wavelength (µm) Wavelength (µm) 14 13 12 11 10 9 8 14 13 12 11 10 9 8

300 300

280 280

260 260

Processes included Classification Cloudless 240 240 Cloudless Volcanic ash

Brightness temperature (K) Volcanic ash Brightness temperature (K) Ice cloud Ice cloud Volcanic ash and ice cloud 220 220

200 200 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 1 1 Wavenumber (cm− ) Wavenumber (cm− )

Fig. 8. (Left plot) Brightness temperature spectra for different locations as measured by IASI on 15 February, 2014, 02:33 UTC, during the Mt. Kelud, Indonesia, eruption. Tentative classiﬁcation of the spectra is given in the legend. See text for details. (Right plot) Simulated brightness temperature spectra using ARTS/uvspec. The atmospheric processes included in the simulations are given in the legend.

945 creasing wavenumber, while the converse is true for the ash 0 spectrum. The simulated ash cloud spectrum (black curve in right plot of Fig. 8) differs from the measured spectrum classiﬁed as ash. Both the simulated and measured ash spec- 50 tra increase in magnitude with increasing wavelength above −1 950 1100 cm , but the simulated spectrum increases more. Be- 100 low about 900 cm−1 the spectral behavior of the measured

and simulated spectra differs. This may be due to either 150 wrong assumptions about the ash type and hence refractive index and/or the mixing of ice with ash. Ice clouds have 200 955 an opposite effect of ash clouds on the brightness temperature between 800-1000 cm−1, whereas above 1075 cm−1 ice 0 100 200 300 400 0 clouds have only a very weak dependence on wavenumber (see Fig. 2 of Gangale et al., 2010). To test if the presence of both ash and ice could reproduce the measured spectrum, 50 960 simulations were made with both an ash cloud and an ice cloud. The altitude and thickness of the clouds were as above, 100 but the ash cloud density was 2×10−4 g/m3 and the ice wa- −2 3 ter content 1.5×10 g/m . The resulting spectrum is shown 150 in maroon in the right plot of Fig. 8. The mixed scene with 965 both ash and ice is seen to well reproduce the measured ash 200 spectrum in the left plot of Fig. 8. 0 100 200 300 400 11.2 Simulated satellite image

Fig. 9 shows a simulated satellite image (top) and the corre- Fig. 9. Top: Simulation of MSG-SEVIRI image. False color composite, where red corresponds to the 1.6 µm channel, green to sponding observation (bottom). Three visible channels of the 0.8 µm and blue to 0.6 µm. The simulation was performed using 970 SEVIRI instrument on the MSG (Meteosat Second Genera- the disort solver with input data from the operational COSMO- tion) satellite were simulated based on input data from the DE forecast for the 15th July 2012, 12 UTC. The axes correspond operational COSMO-DE forecast (Baldauf et al., 2011) of to SEVIRI pixel. Bottom: Corresponding SEVIRI image. Deutscher Wetterdienst for the 15th July 2012, 12 UTC. The C. Emde et al.: The libRadtran software package 17

spatial resolution of the simulation is 2.8 km×2.8 km, that 975 of the SEVIRI observation is 3 km×3 km at the sub-satellite point. A false color composite was generated using the simulated radiance of the 1.6 µm channel for red, the 0.8 µm radiance for green and 0.6 µm radiance for blue. The simulations were performed using the one-dimensional disort I Q

980 solver. The MODIS surface albedo dataset was used (Schaaf 0.00 0.03 et al., 2002) to set the Lambertian surface albedo. The effective radii of liquid clouds were parameterized according to 0.02 Martin et al. (1994), and for the optical properties the mie 0.01 0.01 parameterization was applied. Ice cloud effective radii were mol. atmosphere 985 parameterized according to Wyser (1998) and for the corre- 0.00 0.02 baum v36 sponding optical properties the parameterization 0.01 was used with the general habit mixture. Molecular absorp- 0.12 0.03 tion was included using the reptran parameterization. In 0.08

the false color composite water clouds appear white and 0.05

ocean surface 0.04 990 ice clouds appear blueish, because ice absorbs in the region 0.07 about 1.6 µm. The simulated image looks very similar to the 0.00 observation. A major difference is that the ice clouds in the observation appear more blueish, the reason is that their real 0.00 0.09 optical thickness is larger than in the COSMO-DE forecast. 0.01 0.08 aerosol desert 995 11.3 Polarization 0.07 0.02

The MYSTIC solver can be applied to simulate multi- 0.00 angle multi-spectral polarized radiances using the option 0.14 mc polarisation (Emde et al., 2010). Polarized radia- 0.01 tive transfer using MYSTIC has been validated in extensive 0.12

liquid water cloud 0.02 1000 model intercomparison projects (Kokhanovsky et al., 2010; Emde et al., 2015). 0.10 Fig. 10 shows an example for simulations at wavelengths 0.01 0.14 of 443, 670 and 865 nm; these are measured by the POLDER (Polarization and Directionality of the Earth’s Reflectances) 0.10 0.00 1005 instrument onboard PARASOL (Polarization and Anisotropy 0.06 of Reflectances for Atmospheric Sciences coupled with Ob- ice cloud smooth 0.01 servations from a Lidar) (Deschamps et al., 1994). All sim- 0.02 ulations are for a solar zenith angle of 30◦ and show the re- 0.00 flected radiances (normalized to incoming solar irradiance) 0.06 1010 at the top of the atmosphere in the solar principal plane. The ◦ viewing angle of 30 corresponds to the exact backscattering 0.04 0.01 direction. The angular resolution is 2◦. All simulations are ice cloud rough for the US standard atmosphere. The figure shows the first 0.02 50 25 0 25 50 50 25 0 25 50

and second components of the Stokes vector I and Q; the viewing angle [ ◦ ] viewing angle [ ◦ ] 1015 components U and V are exactly 0 in the principal plane for symmetry reasons. Fig. 10. Stokes vector components I and Q at wavelengths of The ﬁrst row shows the results for a clear atmosphere, 443 nm (blue solid lines), 670 nm (green dashed lines), and 865 nm (red dashed-dotted lines) for various atmospheric setups (see text i.e. Rayleigh scattering and molecular absorption. Here I is for details). The radiances are calculated at the top of the atmo- largest for the shortest wavelength because the Rayleigh scat- ◦ ◦ ◦ −4 sphere for viewing angles from -50 to 50 , where 0 corresponds 1020 tering cross section decreases with λ , where λ is the wave- to the nadir direction. length. The absolute value of Q also increases with increasing Rayleigh scattering cross section. A negative Q means that Rayleigh scattering polarizes perpendicular to the scattering plane, which, for single scattering, corresponds to the 1025 principal plane for this geometry. 18 C. Emde et al.: The libRadtran software package

The second row of the figure shows the same simulation UV irradiances, which decreased during totality by 2 to 3 or- but with an underlying ocean surface, which is modelled ac-1080 ders of magnitude depending on wavelength. cording to Mishchenko and Travis (1997) (bpdf tsang). Fully spherical geometry has also been used to simu- The wind speed was set to 2 m/s. I and Q clearly show the late actinic fluxes at high solar zenith angles up to 92◦ 1030 sun glint which has a maximum at a viewing angle of about (Suminska-Ebersoldt´ et al., 2012). -30◦ and which is highly polarized. The intensity of the sun- Another interesting application is the simulation of polar- glint increases with increasing wavelength since the incom-1085 ized radiance at the surface at twilight, because polarized ing radiance at the surface becomes less diffuse when there radiance measurements at twilight can be used to retrieve is less Rayleigh scattering in the atmosphere. aerosol optical properties (e.g. Saito and Iwabuchi (2015)). 1035 The third row shows the result for desert aerosol as de- As an example we calculated polarized clear sky radiances fined in the OPAC database (aerosol species file for solar depression angles up to 9◦ for the US-standard at- desert), with an underlying Lambertian surface albedo of1090 mosphere and default Rayleigh scattering and absorption set- 0.3. I shows a backscatter peak at 670 and 865 nm. Q looks tings. Fig. 11 shows the result as a function of viewing zenith similar as for Rayleigh scattering, however there are differ- angle. The relative azimuth angle between sun and observer ◦ 1040 ences mainly around the backscatter region. At wavelengths is 0 which means that the observer looks into the direction of 670 and 865 nm, Q has a minimum in the exact backscat- of the sun. We see that the intensity decreases by about four ◦ ter direction and becomes positive for viewing angles around1095 orders of magnitude for solar depression angles between 0 this direction. (sun at horizon) and 9◦ (sun 9◦ below horizon). The degree The fourth row shows a simulation including a water cloud of polarization (not shown) at a viewing angle of 5◦ is more 1045 (wc properties mie) in 2-3 km altitude with an optical than 90%. All results agree to published results by Blattner¨ thickness of 10 and an effective droplet radius of 10 µm. I et al. (1974), which indicates that fully spherical geometry and Q show the glory about the backscatter direction and works correctly in MYSTIC. the rainbow at a viewing angle of about -10◦ corresponding ◦ to a scattering angle of 140 . In Q the rainbow is more pro- 500 nm 700 nm 100 100 1050 nounced than in I because Q is less affected by multiple scattering. The angular resolution shown here is not sufficient to 10-1 10-1 separate the glory from the backscattering peak in I. The sign

of Q in the rainbow region is the same as for Rayleigh scat- -2 -2 10 -2 ◦ 10 0 ◦ -2 ◦ tering whereas it is opposite in the glory region, which means 0 ◦ 2 1055 that the rainbow is polarized perpendicular to the scattering -3 2 ◦ -3 ◦ 10 10 3 ◦ 3 ◦

plane whereas the glory is polarized parallel to the scattering L

π 4 ◦ 4 ◦ plane. 10-4 10-4 The last two rows show simulations with ice clouds, where 5 ◦ 5 ◦ 6 ◦ 6 ◦ we have used the yang2013 parameterization. An ice cloud 10-5 10-5 1060 layer with an optical thickness of 2 was included at an alti- 8 ◦ 8 ◦ tude from 9–10 km. The selected habit was solid column 10-6 10-6 and we performed simulations for smooth crystals and for 9 ◦ 9 ◦

severely rough crystals respectively. The effective crystal 10-7 10-7 20 0 20 40 60 80 100 20 0 20 40 60 80 100 radius in both simulations is 30 µm. The smooth crystals θ [ ◦ ] θ [ ◦ ] 1065 show a backscatter peak in I and a positive Q about the backscatter direction. Also there are some smaller features Fig. 11. Twilight radiance at 500 nm and 700 nm calculated using in I and Q. The radiances (I and Q) for rough crystals are fully spherical geometry for the US-standard atmosphere. The lines smooth functions of viewing angle. This different behaviour are for different solar depression angles. The x-axis corresponds to the viewing zenith angle. has been used to determine the fraction of smooth crystals in 1100 1070 ice clouds from POLDER measurements (Cole et al., 2014).

11.4 Fully spherical geometry 12 Summary

MYSTIC can be operated in fully spherical geometry We have presented the libRadtran software package (version (mc spherical 1D). The implementation of 1D spheri- 2.0.1), which is a comprehensive and powerful collection of cal geometry is described in Emde and Mayer (2007) where tools for radiative transfer simulations of the Earth’s atmo- 1075 it has been used to simulate radiation in the umbral shadow of1105 sphere. It is user-friendly, well-documented and is widely a solar eclipse. A comparison to measurements during the to- used in the scientiﬁc community. We have described vari- tal eclipse in Greece in March 2006 (Kazantzidis et al., 2007) ous new features and parameterizations which have been in- showed a very good agreement for modeled and measured cluded after the ﬁrst publication of libRadtran in 2005. New C. Emde et al.: The libRadtran software package 19

features are for example a vector radiative transfer solver References 1110 and a solver for rotational Raman scattering. The package includes state-of-the-art parameterizations for aerosol and ice Ackerman, M.: UV-solar radiation related to mesospheric pro- cloud optical properties and a newly developed efficient ab-1130 cesses, D. Reidel Publishing Company, edited by G. Fiocco, sorption parameterization. 1971. Alexandrov, M. D., Cairns, B., Emde, C., Ackerman, A. S., and van Diedenhoven, B.: Accuracy assessments of cloud droplet 13 Code availability size retrievals from polarized reflectance measurements by the 1135 research scanning polarimeter, Remote Sens. Environ., 125, 92– 111, doi:10.1016/j.rse.2012.07.012, 2012. 1115 The libRadtran package was initiated about 20 years ago and is still under continuous development. Regularly up- Anderson, G., Clough, S., Kneizys, F., Chetwynd, J., and Shettle, E.: AFGL atmospheric constituent profiles (0-120 km), Tech. dated versions of the package are available from http://www. Rep. AFGL-TR-86-0110, Air Force Geophys. Lab., Hanscom Air libradtran.org. 1140 Force Base, Bedford, Mass., 1986. The website includes all released versions of the package. Baldauf, M., Seifert, A., Forstner,¨ J., Majewski, D., Raschendorfer, 1120 The latest release is version 2.0.1 and includes the source M., , and Reinhardt, T.: Operational convective-scale numerical code, example input files, several tests, and the graphical user weather prediction with the COSMO model: description and sen- interface. Additional data packages containing optical prop- sitivities, Monthly Weather Review, 139, 3887–3905, 2011. erties of clouds and aerosols and the REPTRAN gas absorp-1145 Bass, A. M. and Paur, R. J.: The ultraviolet cross–section of ozone, tion parameterization are also available. The 1D version of I, The measurements, in: Atmospheric Ozone: Proceedings of the Quadrennial Ozone Symposium, edited by Zerefos, C. S. and 1125 MYSTIC is part of the libRadtran public release. Please note that the 3D version of MYSTIC is not part of the libRadtran Ghazi, A., pp. 601–606, D. Reidel, Norwell, Mass., 1985. public release, it is available in joint projects. Baum, B., Heymsfield, A., Yang, P., and Bedka, S.: Bulk scattering 1150 models for the remote sensing of ice clouds. Part 1: Microphysi- cal data and models, J. of Applied Meteorology, 44, 1885–1895, 2005a. Baum, B., Yang, P., Heymsfield, A., Platnick, S., King, M., Hu, Y.- X., and Bedka, S.: Bulk scattering models for the remote sensing 1155 of ice clouds. Part 2: Narrowband models, J. of Applied Meteo- rology, 44, 1896–1911, 2005b. Baum, B. A., Yang, P., Heymsfield, A. J., Bansemer, A., Merrelli, A., Schmitt, C., and Wang, C.: Ice cloud bulk single-scattering property models with the full phase matrix at wavelengths from 1160 0.2 to 100 µm, J. Quant. Spectrosc. Radiat. Transfer, special Is- sue ELS-XIV, 2014. Blattner,¨ W. G., Horak, H. G., Collins, D. G., and Wells, M. B.: Monte Carlo Studies of the Sky Radiation of Twilight, Appl. Opt., 13, 534–547, 1974. 1165 Bodhaine, B. A., Wood, N. B., Dutton, E. G., and Slusser, J. R.: On Rayleigh optical depth calculations, J. Atm. Ocean Technol., 16, 1854–1861, 1999. Bogumil, K., Orphal, J., Voigt, S., Spietz, P., Fleischmann, O. C., Vogel, A., Hartmann, M., Kromminga, H., Bovensmann, H., Fr- 1170 erick, J., and Burrows, J. P.: Measurements of molecular absorption spectra with the SCIAMACHY pre-flight model: instrument characterization and reference data for atmospheric remote- sensing in the 230-2380 nm region, J. Photochem. and Photobio. A: Chem., 157, 167–184, 2003. 1175 Bohren, C. F. and Huffman, D. R.: Absorption and Scattering of Light by Small Particles, John Wiley & Sons, 1983. Buehler, S., John, V., Kottayil, A., Milz, M., and Eriksson, P.: Ef- ficient radiative transfer simulations for a broadband infrared ra- diometer - combining a weighted mean of representative frequen- 1180 cies approach with frequency selection by simulated annealing, JQSRT, 111, 602–615, 2010. Bugliaro, L., Zinner, T., Keil, C., Mayer, B., Hollmann, R., Reuter, M., and Thomas, W.: Validation of cloud property retrievals with simulated satellite radiances: a case study for SEVIRI, Atmos. 1185 Chem. Phys., 11, 5603–5624, doi:10.5194/acp-11-5603-2011, 2011. 20 C. Emde et al.: The libRadtran software package

Buras, R. and Mayer, B.: Efficient unbiased variance reduction Daumont, D., Brion, J., Charbonnier, J., and Malicet, J.: Ozone UV techniques for Monte Carlo simulations of radiative transfer in spectroscopy I: Absorption cross-sections at room temperature, cloudy atmospheres: The solution, J. Quant. Spectrosc. Radiat. J. of Atmospheric Chemistry, 15, 145–155, 1992. 1190 Transfer, 112, 434–447, 2011. Degunther,¨ M. and Meerkotter,¨ R.: Influence of inhomogeneous sur- Buras, R., Dowling, T., and Emde, C.: New secondary-scattering1250 face albedo on UV irradiance: Effect of a stratus cloud, J. Geo- correction in DISORT with increased efficiency for forward scat- phys. Res., 105, 22 755–22 761, 2000. tering, J. Quant. Spectrosc. Radiat. Transfer, 112, 2028–2034, Deschamps, P.-Y., Breon, F.-M., Leroy, M., Podaire, A., Bricaud, 2011. A., Buriez, J.-C., and Seze, G.: The POLDER mission: in- 1195 Burrows, J. P., Dehn, A., Deters, B., Himmelmann, S., Richter, strument characteristics and scientific objectives, IEEE Trans- A., Voigt, S., and Orphal, J.: Atmospheric remote–sensing refer-1255 actions on Geoscience and Remote Sensing, 32, 598–615, ence data from GOME: Part 1. Temperature–dependent absorp- doi:10.1109/36.297978, 1994. tion cross sections of NO2 in the 231–794 nm range, J. Quant. Drusch, M., Bello, U. D., Carlier, S., Colin, O., Fernan- Spectrosc. Radiat. Transfer, 60, 1025–1031, 1998. dez, V., Gascon, F., Hoersch, B., Isola, C., Laberinti, P., 1200 Cahalan, R., Oreopoulos, L., Marshak, A., Evans, K., Davis, A., Martimort, P., Meygret, A., Spoto, F., Sy, O., March- Pincus, R., Yetzer, K., Mayer, B., Davies, R., Ackerman, T.,1260 ese, F., and Bargellini, P.: Sentinel-2: ESA’s Optical H.W., B., Clothiaux, E., Ellingson, R., Garay, M., Kassianov, High-Resolution Mission for {GMES} Operational Ser- E., Kinne, S., Macke, A., O’Hirok, W., Partain, P., Prigarin, S., vices, Remote Sensing of Environment, 120, 25 – 36, Rublev, A., Stephens, G., Szczap, F., Takara, E., Varnai, T., Wen, doi:http://dx.doi.org/10.1016/j.rse.2011.11.026, http://www. 1205 G., and Zhuraleva, T.: The International Intercomparison of 3D sciencedirect.com/science/article/pii/S0034425712000636, the Radiation Codes (I3RC): Bringing together the most advanced1265 Sentinel Missions - New Opportunities for Science, 2012. radiative transfer tools for cloudy atmospheres, Bulletin of the Ehret, G., Kiemle, C., Wirth, M., Amediek, A., Fix, A., American Meteorological Society, 86, 1275–1293, 2005. and Houweling, S.: Space-borne remote sensing of CO2, Cantrell, C. A., Davidson, J. A., McDaniel, A. H., Shetter, R. E., CH4, and N2O by integrated path differential absorption li- 1210 and Calvert, J. G.: Temperature-dependent formaldehyde cross dar: a sensitivity analysis, Applied Physics B, 90, 593– sections in the near-ultraviolet spectral region, J. Phys. Chem.,1270 608, doi:10.1007/s00340-007-2892-3, http://dx.doi.org/10.1007/ 94, 3902–3908, 1990. s00340-007-2892-3, 2008. Chahine, M.: Remote sounding of cloudy atmospheres, I, The single Emde, C. and Mayer, B.: Simulation of solar radiation during a total cloud layer, J. Atmos. Sci., 31, 233–243, 1974. solar eclipse: A challenge for radiative transfer, Atmos. Chem. 1215 Chandrasekhar, S.: Radiative transfer, Oxford Univ. Press, UK, Phys., 7, 2259–2270, 2007. 1950. 1275 Emde, C., Buras, R., Mayer, B., and Blumthaler, M.: The impact of Clarisse, L., Prata, F., Lacour, J.-L., Hurtmans, D., Clerbaux, C., and aerosols on polarized sky radiance: model development, valida- Coheur, P.-F.: A correlation method for volcanic ash detection tion, and applications, Atmos. Chem. Phys., 10, 383–396, 2010. using hyperspectral infrared measurements, Geophys. Res. Lett., Emde, C., Buras, R., and Mayer, B.: ALIS: An efficient method to 1220 37, doi:10.1029/2010GL044828, 2010. compute high spectral resolution polarized solar radiances using Clarisse, L., Coheur, P.-F., Prata, F., Hadji-Lazaro, J., Hurtmans,1280 the Monte Carlo approach, J. Quant. Spectrosc. Radiat. Transfer, D., and Clerbaux, C.: A unified approach to infrared aerosol re- 112, 1622–1631, 2011. mote sensing and type specification, Atmospheric Chemistry and Emde, C., Barlakas, V., Cornet, C., Evans, F., Korkin, S., Physics, 13, 2195–2221, doi:10.5194/acp-13-2195-2013, http: Ota, Y., Labonnote, L. C., Lyapustin, A., Macke, A., 1225 //www.atmos-chem-phys.net/13/2195/2013/, 2013. Mayer, B., and Wendisch, M.: IPRT polarized radia- Clerbaux, C., Boynard, A., Clarisse, L., George, M., Hadji-1285 tive transfer model intercomparison project – Phase Lazaro, J., Herbin, H., Hurtmans, D., Pommier, M., Razavi, A, J. Quant. Spectrosc. Radiat. Transfer, 164, 8–36, A., Turquety, S., Wespes, C., and Coheur, P.-F.: Moni- doi:http://dx.doi.org/10.1016/j.jqsrt.2015.05.007, http://www. toring of atmospheric composition using the thermal in- sciencedirect.com/science/article/pii/S0022407315001922, 1230 frared IASI/MetOp sounder, Atmospheric Chemistry and 2015. Physics, 9, 6041–6054, doi:10.5194/acp-9-6041-2009, http://1290 Eriksson, P., Buehler, S. A., Davis, C. P., Emde, C., and Lemke, O.: www.atmos-chem-phys.net/9/6041/2009/, 2009. ARTS, the atmospheric radiative transfer simulator, Version 2, J. Cole, B. H., Yang, P., Baum, B. A., Riedi, J., and C.-Labonnote, Quant. Spectrosc. Radiat. Transfer, 112, 1551–1558, 2011. L.: Ice particle habit and surface roughness derived from Evans, K. F.: The spherical harmonics discrete ordinate method for 1235 PARASOL polarization measurements, Atmos. Chem. Phys., three–dimensional atmospheric radiative transfer, J. Atmos. Sci., 14, 3739–3750, doi:10.5194/acp-14-3739-2014, http://www.1295 55, 429–446, 1998. atmos-chem-phys.net/14/3739/2014/, 2014. Evans, K. F. and Stephens, G. L.: A new polarized atmospheric ra- Cox, C. and Munk, W.: Measurement of the roughness of the sea diative transfer model, J. Quant. Spectrosc. Radiat. Transfer, 46, surface from photographs of the sun’s glitter, Journal of the Op- 413–423, 1991. 1240 tical Society of America, 44, 838–850, 1954a. Eyre, J. and Menzel, P.: Retrieval of Cloud Parameters from Satel- Cox, C. and Munk, W.: Statistics of the sea surface derived from1300 lite Sounder Data: A Simulation Study, J. of Applied Meteorol- sun glitter, Journal of Marine Research, 13, 198–227, 1954b. ogy, 28, 267–275, 1989. Dahlback, A. and Stamnes, K.: A new spherical model for com- Forster, L., Emde, C., Mayer, B., and Unterstrasser, S.: Effects of puting the radiation field available for photolysis and heating at Three-Dimensional Photon Transport on the Radiative Forcing 1245 twilight, Planet. Space Sci., 39, 671–683, 1991. of Realistic Contrails, J. Atmos. Sci., 69, 2243–2255, 2012. C. Emde et al.: The libRadtran software package 21

1305 Forster, P. M., Fomichev, V. I., Rozanov, E., Cagnazzo, C., heur, P.-F., Collard, A., Crevoisier, C., Dufour, G., Edwards, D., Jonsson, A. I., Langematz, U., Fomin, B., Iacono, M. J.,1365 Faijan, F., Fourrie,´ N., Gambacorta, A., Goldberg, M., Guidard, Mayer, B., Mlawer, E., Myhre, G., Portmann, R. W., Akiyoshi, V., Hurtmans, D., Illingworth, S., Jacquinet-Husson, N., Kerzen- H., Falaleeva, V., Gillett, N., Karpechko, A., Li, J., Lemen- macher, T., Klaes, D., Lavanant, L., Masiello, G., Matricardi, nais, P., Morgenstern, O., Oberlaender, S., Sigmond, M., M., McNally, A., Newman, S., Pavelin, E., Payan, S., Pequignot,´ 1310 and Shibata, K.: Evaluation of radiation scheme performance E., Peyridieu, S., Phulpin, T., Remedios, J., Schlussel,¨ P., Se- within chemistry climate models, J. Geophys. Res., 116,1370 rio, C., Strow, L., Stubenrauch, C., Taylor, J., Tobin, D., Wolf, doi:10.1029/2010JD015361, 2011. W., and Zhou, D.: Hyperspectral Earth Observation from IASI: Fu, Q.: An accurate parameterization of the solar radiative proper- Five Years of Accomplishments, Bulletin of the American Me- ties of cirrus clouds for climate models, J. of Climate, 9, 2058– teorological Society, 93, 347–370, doi:10.1175/BAMS-D-11- 1315 2082, 1996. 00027.1, http://dx.doi.org/10.1175/BAMS-D-11-00027.1, 2011. Fu, Q. and Liou, K.: On the correlated k-distribution method for ra-1375 Hu, Y. X. and Stamnes, K.: An accurate parameterization of the diative transfer in nonhomogeneous atmospheres, J. Atmos. Sci., radiative properties of water clouds suitable for use in climate 49, 2139–2156, 1992. models, J. of Climate, 6, 728–742, 1993. Fu, Q. and Liou, K.: Parameterization of the radiative properties of Ivanova, D., Mitchell, D. L., Arnott, W. P., and Poellot, M.: A GCM 1320 cirrus clouds, J. Atmos. Sci., 50, 2008–2025, 1993. parameterization for bimodal size spectra and ice mass removal Fu, Q., Yang, P., and Sun, W. B.: An accurate parameterization of1380 rates in mid-latitude cirrus clouds, Atmospheric Research, 59-60, the infrared radiative properties of cirrus clouds for climate mod- 89–113, 2001. els, J. of Climate, 11, 2223–2237, 1998. Kato, S., Ackerman, T. P., Mather, J. H., and Clothiaux, E.: The k– Gangale, G., Prata, A. J., and Clarisse, L.: The infrared spectral sig- distribution method and correlated–k approximation for a short- 1325 nature of volcanic ash determined from high-spectral resolution wave radiative transfer model, J. Quant. Spectrosc. Radiat. Trans- satellite measurements, Remote Sens. Environ., 114, 414–425,1385 fer, 62, 109–121, 1999. 2010. Kazantzidis, A., Bais, A., Emde, C., Kazadzis, S., and Zerefos, Gasteiger, J., Groß, S., Freudenthaler, V., and Wiegner, M.: Vol- C.: Attenuation of global ultraviolet and visible irradiance over canic ash from Iceland over Munich: mass concentration re- Greece during the total solar eclipse of 29 March 2006, Atmos. 1330 trieved from ground-based remote sensing measurements, At- Chem. Phys. Discuss., 7, 13 475–13 501, 2007. mos. Chem. Phys., 11, 2209–2223, doi:10.5194/acp-11-2209-1390 Key, J. R., Yang, P., Baum, B. A., and Nasiri, S. L.: Parameteriza- 2011, 2011. tion of shortwave ice cloud optical properties for various parti- Gasteiger, J., Emde, C., Mayer, B., Buehler, S. A., and Lemke, O.: cle habits, J. Geophys. Res., 107, doi:10.1029/2001JD000 742, Representative wavelengths absorption parameterization applied 2002. 1335 to satellite channels and spectral bands, J. Quant. Spectrosc. Ra- Klinger, C. and Mayer, B.: Three-dimensional Monte Carlo calcu- diat. Transfer, 148, 99–115, 2014. 1395 lation of atmospheric thermal heating rates, J. Quant. Spectrosc. Greenblatt, G. D., Orlando, J. J., Burkholder, J. B., and Ravis- Radiat. Transfer, 144, 123–136, doi:10.1016/j.jqsrt.2014.04.009, hankara, A. R.: Absorption measurements of oxygen between 2014. 330 and 1140 nm, J. Geophys. Res., 95, 18 577–18 582, 1990. Koepke, P., Gasteiger, J., and Hess, M.: Technical Note: Optical 1340 Guanter, L., Alonso, L., Gomez-Chova,´ L., Meroni, M., Preusker, properties of desert aerosol with non-spherical mineral parti- R., Fischer, J., and Moreno, J.: Developments for vegetation fluo-1400 cles: data incorporated to OPAC, Atmos. Chem. Phys., 15, 5947– rescence retrieval from spaceborne high-resolution spectrometry 5956, doi:10.5194/acp-15-5947-2015, 2015. in the O2-A and O2-B absorption bands, J. Geophys. Res., 115, Kokhanovsky, A. A., Budak, V. P., Cornet, C., Duan, M., Emde, 2463–2479, doi:doi:10.1029/2009JD013716, 2010. C., Katsev, I. L., Klyukov, D. A., Korkin, S. V., C-Labonnote, 1345 Hansen, J. E. and Travis, L. D.: Light scattering in planetary atmo- L., Mayer, B., Min, Q., Nakajima, T., Ota, Y., Prikhach, A. S., spheres, Space Science Reviews, 16, 527–610, 1974. 1405 Rozanov, V. V., Yokota, T., and Zege, E. P.: Benchmark results in Hapke, B.: Theory of reflectance and emittance spectroscopy, New vector atmospheric radiative transfer, J. Quant. Spectrosc. Radiat. York: Cambridge University Press, 1993. Transfer, 111, 1931–1946, 2010. Hess, M., Koepke, P., and Schult, I.: Optical Properties of Aerosols Kokhanovsky, A. A., Deuze, J. L., Diner, D. J., Dubovik, O., Ducos, 1350 and Clouds: The Software Package OPAC, Bulletin of the Amer- F., Emde, C., Garay, M. J., Grainger, R. G., Heckel, A., Herman, ican Meteorological Society, 79, 831–844, 1998. 1410 M., Katsev, I. L., Keller, J., Levy, R., North, P. R. J., Prikhach, Heymsfield, A. J., Bansemer, A., Field, P. R., Durden, S. L., Stith, A. S., Rozanov, V. V., Sayer, A. M., Ota, Y., Tanre, D., Thomas, J. L., Dye, J. E., Hall, W., and A.Grainger, C.: Observations and G. E., and Zege, E. P.: The inter-comparison of major satellite Parameterizations of Particle Size Distributions in Deep Tropi- aerosol retrieval algorithms using simulated intensity and polar- 1355 cal Cirrus and Stratiform Precipitating Clouds: Results from In ization characteristics of reflected light, Atmos. Meas. Tech., 3, Situ Observations in TRMM Field Campaigns, J. Atmos. Sci.,1415 909–932, doi:10.5194/amt-3-909-2010, 2010. 59, 3457–3491, 2002. Kostka, P. M., Weissmann, M., Buras, R., Mayer, B., and Stiller, Heymsfield, A. J., Schmitt, C., and Bansemer, A.: Ice cloud parti- O.: Observation Operator for Visible and Near-Infrared Satel- cle size distributions and pressure dependent terminal velocities lite Reflectances, J. Atm. Ocean Technol., 31, 1216–1233, ◦ ◦ 1360 from in situ observations at temperatures from 0 to -86 C, J. doi:10.1175/JTECH-D-13-00116.1, 2014. Atmos. Sci., 70, 4123–4154, 2013. 1420 Kotchenova, S. Y., Vermote, E. F., Matarrese, R., and Frank Hilton, F., Armante, R., August, T., Barnet, C., Bouchard, A., J. Klemm, J.: Validation of a vector version of the 6S radiative Camy-Peyret, C., Capelle, V., Clarisse, L., Clerbaux, C., Co- transfer code for atmospheric correction of satellite data. Part I: 22 C. Emde et al.: The libRadtran software package

Path radiance, Appl. Opt., 45, 6762–6774, 2006. sciencedirect.com/science/article/pii/S0034425703003808, Kreuter, A., Buras, R., Mayer, B., Webb, A., Kift, R., Bais, A., 2004. 1425 Kouremeti, N., and Blumthaler, M.: Solar irradiance in the het- Malicet, J., Daumont, D., Charbonnier, J., Parisse, C., Chakir, A., erogeneous albedo environment of the Arctic coast: measure-1485 and Brion, J.: Ozone UV spectroscopy. II. Absorption cross– ments and a 3-D model study, Atmos. Chem. Phys., 14, 5989– sections and temperature dependence, J. of Atmospheric Chem- 6002, doi:10.5194/acp-14-5989-2014, 2014. istry, 21, 263–273, 1995. Kylling, A. and Stamnes, K.: Efficient yet accurate solution of the Martin, G. M., Johnson, D. W., and Spic, A.: The measurement and 1430 linear transport equation in the presence of internal sources: the parameterization of effective radius of droplets in warm stratocu- exponential–linear–in–depth approximation, J. Com. Phys., 102,1490 mulus clouds, J. Atmos. Sci., 51, 1823–1842, 1994. 265–276, 1992. Mayer, B.: Radiative transfer in the cloudy atmosphere, European Kylling, A., Stamnes, K., and Tsay, S.-C.: A reliable and efficient Physical Journal Conferences, 1, 75–99, 2009. two–stream algorithm for spherical radiative transfer: documen- Mayer, B. and Kylling, A.: Technical note: The libRadtran software 1435 tation of accuracy in realistic layered media , J. of Atmospheric package for radiative transfer calclations – description and exam- Chemistry, 21, 115–150, 1995. 1495 ples of use, Atmos. Chem. Phys., 5, 1855–1877, 2005. Kylling, A., Mayer, B., and Blumthaler, M.: Technical Note: A new Mayer, B., Hoch, S. W., and Whiteman, C. D.: Validating the MYS- discrete ordinate first-order rotational Raman scattering radiative TIC three-dimensional radiative transfer model with observa- transfer model – implementation and first results, Atmos. Chem. tions from the complex topography of Arizona’s Meteor Crater, 1440 Phys., 11, 10 471–10 485, doi:10.5194/acp-11-10471-2011, http: Atmos. Chem. Phys., 10, 8685–8696, 2010. //www.atmos-chem-phys.net/11/10471/2011/, 2011. 1500 Menzel, W., Smith, W., and Stewart, T.: Improved cloud motion Kylling, A., Buras, R., Eckhardt, S., Emde, C., Mayer, B., and Stohl, wind vector and altitude assignment using VAS, J. of Applied A.: Simulation of SEVIRI infrared channels: a case study from Meteorology, 22, 377–384, 1983. the Eyjafjallajokull¨ April/May 2010 eruption, Atmospheric Mea- Miller, J. R., Berger, M., Goulas, Y., Jacquemoud, S., Louis, J., Mo- 1445 surement Techniques, 6, 649–660, doi:10.5194/amt-6-649-2013, hammed, G., Moise, N., Moreno, J., Moya, I., Pedros,´ R., Ver- 2013. 1505 hoef, W., and Zarco-Tejada, P.: Development of a Vegetation Flu- Kylling, A., Kristiansen, N., Stohl, A., Buras-Schnell, R., Emde, orescence Canopy Model, Tech. rep., ESA–ESTEC, Noordwijk, C., and Gasteiger, J.: A model sensitivity study of the impact of the Netherlands, http://www.ias.csic.es/fluormod/, 2005. clouds on satellite detection and retrieval of volcanic ash, Atmos. Minschwaner, K., Anderson, G. P., Hall, L. A., and Yoshino, K.: 1450 Meas. Tech., 8, 1935–1949, doi:10.5194/amt-8-1935-2015, http: Polynomial coefficients for calculating O2 Schumann-Runge //www.atmos-meas-tech.net/8/1935/2015/, 2015. 1510 cross sections at 0.5 cm-1 resolution, J. Geophys. Res., 97, Kylling, A., Mayer, B., and Blumthaler, M.: Technical Note: A new 10 103–10 108, 1992. discrete ordinate first-order rotational Raman scattering radia- Mishchenko, M., Lacis, A., and Travis, L.: Errors induced tive transfer model - implementation and first results, Atmos. by the neglect of polarization in radiance calculations for 1455 Chem. Phys., 11, 10 471–10 485, doi:10.5194/acp-11-10471- rayleigh-scattering atmospheres, J. Quant. Spectrosc. Radiat. 2011, 2011. 1515 Transfer, 51, 491 – 510, doi:http://dx.doi.org/10.1016/0022- Lee, D., Pitari, G., Grewe, V., Gierens, K., Penner, J., Petzold, 4073(94)90149-X, http://www.sciencedirect.com/science/ A., Prather, M., Schumann, U., Bais, A., Berntsen, T., Iachetti, article/pii/002240739490149X, 1994. D., Lim, L., and Sausen, R.: Transport impacts on atmosphere Mishchenko, M. I. and Travis, L. D.: Satellite retrieval of aerosol 1460 and climate: Aviation, Atmospheric Environment, 44, 4678 – properties over the ocean using polarization as well as inten- 4734, doi:http://dx.doi.org/10.1016/j.atmosenv.2009.06.005,1520 sity of reflected sunlight, J. Geophys. Res., 102, 16 989–17 013, http://www.sciencedirect.com/science/article/pii/ 1997. S1352231009004956, transport Impacts on Atmosphere Mishchenko, M. I. and Travis, L. D.: Capabilities and limitations and Climate: The {ATTICA} Assessment Report, 2010. of a current Fortran implementation of the T-Matrix method for 1465 Lohmann, S., Schillings, C., Mayer, B., and Meyer, R.: randomly oriented, rotationally symmetric scatterers, J. Quant. Long-term variability of solar direct and global ra-1525 Spectrosc. Radiat. Transfer, 60, 309–324, 1998. diation derived from {ISCCP} data and comparison Mishchenko, M. I., Travis, L., and Lacis, A.: Scattering, Absorp- with reanalysis data, Solar Energy, 80, 1390 – 1401, tion, and Emission of Light by Small Particles, Cambridge Uni- doi:http://dx.doi.org/10.1016/j.solener.2006.03.004, http://www. versity Press, 2002. 1470 sciencedirect.com/science/article/pii/S0038092X0600082X, eu- Mishchenko, M. I., Cairns, B., Kopp, G., Schueler, C. F., Fafaul, ropean Solar Conference (EuroSun 2004) EuroSun Conference1530 B. A., Hansen, J. E., Hooker, R. J., Itchkawich, T., Mar- 2004, 2006. ing, H. B., and Travis, L. D.: Accurate Monitoring of Terres- Lucht, W., Schaaf, C., and Strahler, A.: An algorithm for the re- trial Aerosols and Total Solar Irradiance: Introducing the Glory trieval of albedo from space using semiempirical BRDF mod- Mission, Bulletin of the American Meteorological Society, 88, 1475 els, Geoscience and Remote Sensing, IEEE Transactions on, 38, doi:10.1175/BAMS-88-5-677, 2007. 977–998, doi:10.1109/36.841980, 2000. 1535 Mitchell, D. L., Chai, S. K., Liu, Y.,Heymsfield, A. J., and Dong, Y.: Maignan, F., Breon, F.-M., and Lacaze, R.: Bidirectional re- Modeling Cirrus Clouds. Part I: Treatment of Bimodal Size Spec- flectance of Earth targets: evaluation of analytical models using tra and Case Study Analysis., J. Atmos. Sci., 53, 2952–2966, a large set of spaceborne measurements with emphasis on the 1996. 1480 Hot Spot, Remote Sensing of Environment, 90, 210 – 220, Mitchell, D. L., Macke, A., and Liu, Y.: Modeling Cirrus Clouds. doi:http://dx.doi.org/10.1016/j.rse.2003.12.006, http://www.1540 Part II: Treatment of radiative properties, J. Atmos. Sci., 53, C. Emde et al.: The libRadtran software package 23

2967–2988, 1996. 1600 diat. Transfer, 96, 139–204, 2005. Molina, L. T. and Molina, M. J.: Absolute absorption cross sections Roujean, J.-L., Leroy, M., and Deschamps, P.: A bidirectional re- of ozone in the 185 to 350 nm wavelength range, J. Geophys. flectance model of the Earth’s surface for the correction of re- Res., 91, 14 501–14 508, 1986. mote sensing data, J. Geophys. Res., 97, 20 455–20 468, 1992. 1545 Nakajima, T. and Tanaka, M.: Effect of wind-generated waves on Saito, M. and Iwabuchi, H.: A new method of measur- the transfer of solar radiation in the atmosphere-ocean system, J.1605 ing aerosol optical properties from digital twilight pho- Quant. Spectrosc. Radiat. Transfer, 29, 521–537, 1983. tographs, Atmospheric Measurement Techniques Dis- Nicolet, M.: On the molecular scattering in the terrestrial atmo- cussions, 8, 191–234, doi:10.5194/amtd-8-191-2015, sphere: An empirical formula for its calculation in the homo- http://www.atmos-meas-tech-discuss.net/8/191/2015/, 2015. 1550 sphere, Planet. Space Sci., 32, 1467–1468, 1984. Schaaf, C. B., Gao, F., Strahler, A. H., Lucht, W., Li, X., Tsang, Ogawa, S. and Ogawa, M.: Absorption cross sections of O2 (a 1Dg)1610 T., Strugnell, N. C., Zhang, X., Jin, Y., Muller, J.-P., Lewis, and O2(X 3Sg-) in the region from 1087 to 1700 A,˚ Can. J. Phys., P., Barnsley, M., Hobson, P., Disney, M., Roberts, G., Dun- 53, 1845–1852, 1975. derdale, M., Doll, C., d’Entremont, R. P., Hu, B., Liang, S., Priv- Painemal, D. and Zuidema, P.: Assessment of MODIS cloud ef- ette, J. L., and Roy, D.: First operational BRDF, albedo nadir 1555 fective radius and optical thickness retrievals over the South- reflectance products from {MODIS}, Remote Sensing of En- east Pacific with VOCALS-REx in situ measurements, JOUR-1615 vironment, 83, 135 – 148, doi:http://dx.doi.org/10.1016/S0034- NAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES, 116, 4257(02)00091-3, http://www.sciencedirect.com/science/article/ doi:10.1029/2011JD016155, 2011. pii/S0034425702000913, the Moderate Resolution Imaging Penndorf, R.: Tables of the refractive index for standard air and the Spectroradiometer (MODIS): a new generation of Land Surface 1560 Rayleigh scattering coefficient for the spectral region between Monitoring, 2002. 0.2 and 20.0 µ and their application to atmospheric optics, J. Opt.1620 Schreier, F.: Optimized evaluation of a large sum of functions using Soc. Am., 47, 176–182, 1957. a three-grid approach, Computer Physics Communications, 174, Pierluissi, J. H. and Peng, G.-S.: New molecular transmission 783–792, 2006. band models for LOWTRAN, Optical Engineering, 24, 541–547, Schreier, F. and Bottger,¨ U.: MIRART, a line-by-line code for in- 1565 1985. frared atmospheric radiation computations incl. derivatives, At- Pollack, J. B., Toon, O. B., and Khare, B. N.: Optical properties of1625 mos. Oceanic Opt., 16, 262 – 268, 2003. some terrestrial rocks and glasses, ICARUS, 19, 372–389, 1973. Schreier, F. and Kohlert, D.: Optimized implementations of ratio- Rahman, H., Pinty, B., and Verstraete, M. M.: Coupled surface– nal approximations–a case study on the Voigt and complex error atmosphere reflectance (CSAR) model 2. semiempirical surface function, Computer Physics Communications, 179, 457 – 465, 1570 model usable with NOAA advanced very high resolution ra- 2008. diometer data, J. Geophys. Res., 98, 20,791–20,801, 1993. 1630 Schulmann, T., Katurji, M., and Zawar-Reza, P.: Seeing through Rannou, P., Cours, T., Mouelic,´ S. L., Rodriguez, S., Sotin, C., shadow: Modelling surface irradiance for topographic correc- Drossart, P., and Brown, R.: Titan haze distribution and optical tion of Landsat ETM plus data, ISPRS J. Photogrammetry Rem. properties retrieved from recent observations, Icarus, 208, 850– Sens., 99, 14–24, doi:10.1016/j.isprsjprs.2014.10.004, 2015. 1575 867, doi:http://dx.doi.org/10.1016/j.icarus.2010.03.016, 2010. Seckmeyer, G., Pissulla, D., Glandorf, M., Henriques, D., Johnsen, Reinhardt, B., Buras, R., Bugliaro, L., Wilbert, S., and Mayer, B.:1635 B., Webb, A., Siani, A.-M., Bais, A., Kjeldstad, B., Brogniez, Determination of circumsolar radiation from Meteosat Second C., Lenoble, J., Gardiner, B., Kirsch, P., Koskela, T., Kau- Generation, Atmos. Meas. Tech., 7, 823–838, doi:10.5194/amt- rola, J., Uhlmann, B., Slaper, H., den Outer, P., Janouch, M., 7-823-2014, 2014. Werle, P., Groebner, J., Mayer, B., de la Casiniere, A., Simic, 1580 Ricchiazzi, P., Yang, S., Gautier, C., and Sowle, D.: SBDART: A S., and Carvalho, F.: Variability of UV irradiance in Europe, research and Teaching software tool for plane-parallel radiative1640 PHOTOCHEMISTRY AND PHOTOBIOLOGY, 84, 172–179, transfer in the Earth’s atmosphere, Bulletin of the American Me- doi:10.1111/j.1751-1097.2007.00216.x, 2008. teorological Society, 79, 2101–2114, 1998. Shettle, E.: Models of aerosols, clouds and precipitation for atmo- Rinehart, R.: Radar for meteorologists, Rinehart Publications, fifth spheric propagation studies, in: Atmospheric propagation in the 1585 edition edn., 2010. uv, visible, ir and mm-region and related system aspects, no. 454 Roeckner, E., Arpe, K., Bengtsson, L., Christoph, M., Claussen,1645 in AGARD Conference Proceedings, 1989. M., Dumenil,¨ L., Esch, E., Giorgetta, M., Schlese, U., and Smith, W. and Platt, C.: Intercomparison of radiosonde, ground- Schulzweida, U.: The atmospheric general circulation model based laser, and satellite-deduced cloud heights, J. of Applied ECHAM-4: model description and simulation of present-day cli- Meteorology, 17, 1796–1802, 1978. 1590 mate, Tech. rep., Max Planck-Institut fur¨ Meteorologie, Report Smith, W., Woolf, H., and Jacob, W.: A regression method for ob- No. 218, 1996. 1650 taining real-time temperature and geopotential height profiles Rothman, L. S., Jacquemart, D., Barbe, A., Benner, D. C., Birk, from satellite spectrometer measurements and its application M., Brown, L. R., Carleer, M. R., Chackerian Jr., C., Chance, to Nimbus-3 SIRS observations, Monthly Weather Review, 98, K., Coudert, L. H., Dana, V., Devi, V. M., Flaud, J. ., Gamache, 604–611, 1970. 1595 R. R., Goldman, A., Hartmann, J. ., Jucks, K. W., Maki, A. G., Stamnes, K., Tsay, S.-C., Wiscombe, W., and Jayaweera, K.: Nu- Mandin, J. ., Massie, S. T., Orphal, J., Perrin, A., Rinsland, C. P.,1655 merically stable algorithm for discrete–ordinate–method radia- Smith, M. A. H., Tennyson, J., Tolchenov, R. N., Toth, R. A., tive transfer in multiple scattering and emitting layered media, Vander Auwera, J., Varanasi, P., and Wagner, G.: The HITRAN Appl. Opt., 27, 2502–2509, 1988. 2004 molecular spectroscopic database, J. Quant. Spectrosc. Ra- 24 C. Emde et al.: The libRadtran software package

Stamnes, K., Tsay, S.-C., Wiscombe, W., and Laszlo, I.: DISORT, a Wyser, K.: The effective radius in ice clouds, J. of Climate, 11, General-Purpose Fortran Program for Discrete-Ordinate-Method 1793–1802, 1998. 1660 Radiative Transfer in Scattering and Emitting Layered Media: Yang, P., Wei, H., Huang, H.-L., Baum, B. A., Hu, Y. X., Kattawar, Documentation of Methodology, Tech. rep., Dept. of Physics and1720 G. W., Mishchenko, M. I., and Fu, Q.: Scattering and absorp- Engineering Physics, Stevens Institute of Technology, Hoboken, tion property database for nonspherical ice particles in the near- NJ 07030, 2000. through far-infrared spectral region, Appl. Opt., 44, 5512–5523, Suminska-Ebersoldt,´ O., Lehmann, R., Wegner, T., Grooß, J.-U., 2005. 1665 Hosen,¨ E., Weigel, R., Frey, W., Griessbach, S., Mitev, V., Yang, P., Bi, L., Baum, B. A., Liou, K.-N., Kattawar, G., and Emde, C., Volk, C. M., Borrmann, S., Rex, M., Stroh, F., and1725 Mishchenko, M.: Spectrally consistent scattering, absorption, von Hobe, M.: ClOOCl photolysis at high solar zenith an- and polarization properties of atmospheric ice crystals at wave- gles: analysis of the RECONCILE self-match ﬂight, Atmos. lengths from 0.2 µm to 100 µm, J. Atmos. Sci., pp. 330–347, Chem. Phys., 12, 1353–1365, doi:10.5194/acp-12-1353-2012, 2013. 1670 http://www.atmos-chem-phys.net/12/1353/2012/, 2012. Yoshino, K., Cheung, A. S.-C., Esmond, J. R., Parkinson, W. H., Theys, N., Van Roozendael, M., Hendrick, F., Fayt, C., Her-1730 Freeman, D. E., Guberman, S. L., Jenouvrier, A., Coquart, B., mans, C., Baray, J.-L., Goutail, F., Pommereau, J.-P., and and Merienne, M. F.: Improved absorption cross sections of oxy- De Maziere,` M.: Retrieval of stratospheric and tropospheric gen in the wavelength region 205 - 240 nm of the Herzberg con- BrO columns from multi-axis DOAS measurements at Re- tinuum, Planet. Space Sci., 36, 1469–1475, 1988. ◦ ◦ 1675 union Island (21 S, 56 E), Atmospheric Chemistry and Yoshino, K., Esmond, J. R., Sun, Y., Parkinson, W. H., Ito, K., Physics, 7, 4733–4749, doi:10.5194/acp-7-4733-2007, http://1735 and Matsui, T.: Absorption cross section measurements of car- www.atmos-chem-phys.net/7/4733/2007/, 2007. bon dioxide in the wavelength region 118.7 – 175.5 nm and the Tsang, L., Kong, J. A., and Shin, R. T.: Theory of Microwave Re- temperature dependence, J. Quant. Spectrosc. Radiat. Transfer, mote Sensing, John Wiley, New York, 1985. 55, 53–60, 1996. 1680 van de Hulst, H. C.: Light Scattering by Small Particles, Dover, Yoshino, K., Parkinson, W. H., Ito, K., and Matsui, T.: Absolute ab- 1981. 1740 sorption cross-section measurements of Schumann-Runge con- Vermote, E. F., Tanre,´ D., Deuze,´ J. L., Herman, M., and Mocrette, tinuum of O2 at 90 and 295 K, J. Mol. Spectrosc., 229, 238–243, J.-J.: Second simulation of the satellite signal in the solar spec- 2005. trum, 6S: and overview, IEEE Transactions on Geoscience and Zdunkowski, W., Trautmann, T., and Bott, A., eds.: Radiation in the 1685 Remote Sensing, 35, 675–686, 1997. Atmosphere, Cambridge U. Press, Cambridge, UK, 2007. Wahner, A., Tyndall, G. S., and Ravishankara, A. R.: Absorp-1745 Zinner, T., Wind, G., Platnick, S., and Ackerman, A. S.: Testing tion cross sections for symmetric chlorine dioxide as a func- remote sensing on artiﬁcial observations: impact of drizzle and tion of temperature in the wavelength range 240–480nm, J. Phys. 3-D cloud structure on effective radius retrievals, Atmos. Chem. Chem., 91, 2734—-2738, 1987. Phys., 10, 9535–9549, 2010. 1690 Wahner, A., Ravishankara, A. R., Sander, S. P., and Friedl, R. R.: Absorption cross-section of BrO between 312 and 385 nm at 298 and 223K, Chem. Phys. Lett., 152, 507–512, 1988. Wandji Nyamsi, W., Arola, A., Blanc, P., Lindfors, A. V., Cesnulyte, Appendix A V., Pitkanen,¨ M. R. A., and Wald, L.: Technical Note: A novel

1695 parameterization of the transmissivity due to ozone absorption1750 Ice crystal optical properties parameterizations in the k-distribution method and correlated-k approximation of Kato et al. (1999) over the UV band, Atmospheric Chemistry and The parameterization yang2013 is based on the single scat- Physics, 15, 7449–7456, doi:10.5194/acp-15-7449-2015, http:// tering data by Yang et al. (2013). It is available for nine habits www.atmos-chem-phys.net/15/7449/2015/, 2015. and three roughness parameters. It includes full phase matri- 1700 Wanner, W., Strahler, A., Hu, B., Lewis, P., Muller, J.-P., Li, X., ces for the spectral range from 200 nm to 99 µm. The hey Barker Schaaf, C., and Barnsley, M.: Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS1755 (Hong, Emde, Yang) parameterization is available for six in- and MISR data: Theory and algorithm, J. Geophys. Res., 102, dividual smooth habits and includes the full phase matrices 17 143–17 161, 1997. for the wavelength region from 0.2 to 5 µm. The single scat- 1705 Warren, S. G.: Optical constants of ice from the ultraviolet to the tering properties for the six ice crystal habits have been gen- microwave, Applied Optics, 23, 1206–1225, 1984. erated by Hong Gang based on the improved geometrical op- Weinzierl, B., Sauer, D., Minikin, A., Reitebuch, O., Dahlkoet-1760 tics method (IGOM), the same which is applied in Yang et al. ter, F., Mayer, B., Emde, C., Tegen, I., Gasteiger, J., Petzold, (2013). A., Veira, A., Kueppers, U., and Schumann, U.: On the visi- In order to obtain bulk scattering properties (required by 1710 bility of airborne volcanic ash and mineral dust from the pi- the RTE solver) the single scattering properties need to be in- lot’s perspective in flight, Phys. Chem. Earth, 45-46, 87–102, tegrated over the particle size distribution. In reality the size doi:10.1016/j.pce.2012.04.003, 2012. 1765 distributions are highly variable, for radiative transfer sim- Wiscombe, W.: Improved Mie scattering algorithms, Appl. Opt., 19, 1505–1509, 1980. ulations they are often approximated by simple gamma dis- 1715 WMO: Atmospheric Ozone 1985, Tech. rep., WMO Report No. 16, tributions (e.g. Evans, 1998; Heymsfield et al., 2002; Baum 1986. et al., 2005a,b) or bi-modal gamma distributions (Mitchell et al., 1996; Ivanova et al., 2001). We assume a gamma size C. Emde et al.: The libRadtran software package 25

1770 distribution to compute the bulk scattering properties as for each scattering angle θ and for six matrix elements (denoted the water cloud properties (compare Eq. 4): by index i) needed to describe the scattering process by ran-

1 domly oriented nonspherical particles (see e.g. van de Hulst, b −3 re n(re) = Nre exp − (A1)1815 1981)): ab R Lmax Here re is a measure of the particle size (the radius in case A(L)P (L,i,θ)ω0(L)Qext(L)n(L)dL Lmin hP (reff ,i,θ)i = of spherical particles) and N is the normalization constant R Lmax A(L) ω0(L)Qext(L)n(L)dL 1775 so that the integral over the distribution yields the number of Lmin particles in a unit volume. For spherical particles the param- (A6) eters a and b correspond to the effective radius reff and to the Optical properties for a general habit mixture ghm have effective variance veff , respectively. Typical values of cirrus also been calculated for the hey parameterization following cloud size distributions for b are in the range between 0.1 and the mixing “recipe” suggested by Baum et al. (2005b). 1780 0.5 (Evans, 1998; Heymsfield et al., 2002). In the following we take a fixed value of b = 0.25. We define the effective particle size re(L) for an individual ice crystal as follows (Yang1820 Appendix B et al., 2005): Description of TZS solver 3 V (L) re(L) = (A2) 4 A(L) This solver is based on the zero scattering approximation and can be used to calculate clear sky or “black cloud” radiances 1785 Here L is the maximum dimension of a nonspherical ice at the top of the atmopshere (TOA) in the thermal spectral crystal and A and V are the mean projected area and the vol- 1825 range. Without scattering the formal solution of the radiative ume of the particle, respectively. 2r (L) corresponds to the e transfer equation for the upward intensity (radiance) at TOA “effective distance”, i.e. the representative distance a photon I (τ = 0,µ,φ) at a given frequency ν reduces to travels through an ice crystal without experiencing internal ν 1790 reflections and refraction (Mitchell et al., 1996). The effec- ∗ ∗ Iν (τ = 0,µ,φ) = Iν (τ ,µ,φ)exp(−τ /µ) tive radius of a size distribution is generally defined as: τ ∗ Z R Lmax dτ V (L)n(L)dL 1830 + Bν (τ)exp(−τ/µ) . (B1) 3 Lmin reff = (A3) µ 4 R Lmax A(L)n(L)dL 0 Lmin Here we used the (vertical) absorption optical thickness τ In order to obtain bulk scattering properties which can be measured from top of atmosphere as the vertical coordinate used for radiative transfer calculations, we pre-calculate bulk such that τ = 0 at TOA and τ = τ ∗ at the surface. Variables 1795 optical properties on a specified equidistant effective radius 1835 µ and φ denote the cosine of the zenith angle and the azimuth grid including values from 5 to 90 µm in steps of 5 µm. angle respectively. Planck’s function at a given frequency ν Now using Eq. (A3) we iteratively find the parameter a of the is represented by Bν (τ) and its temperature dependence is size distribution which results in the desired effective radius. contained implicitly in τ. The bulk optical properties are then calculated by integration The first term on the right hand side in Eq. B1 represents 1800 over the gamma distributions with the parameters b=0.25 and 1840 the contribution of the surface and the second one the con- the iteratively obtained a depending on the effective radius. tribution of the atmosphere. The surface contribution can be libRadtran requires the extinction coefficient normalized to written as 1 g/m3 ice: ∗ ∗ Iν (τ ,µ,φ) = s Bν (τ )+ R Lmax A(L)Qext(L)n(L)dL ∗ Lmin 1 τ hβext(reff )i = L (A4) Z Z ρR max V (L)n(L)dL ∗ Lmin 1845 + 2(1 − s) Bν (τ)exp(−(τ − τ)/µ)dτdµ (B2) 0 0 1805 Here Qext(L) is the extinction efficiency, ρ is the density of ice, and n(L) is the gamma size distribution which cor- with the first term representing the emission of the surface responds to the effective radius reff . The single scattering (s=surface emissivity) and the second one the reflection at albedo hω0i is calculated as follows: the surface of the radiation emitted by the atmosphere toward 1850 the surface. The factor 2 comes from the integration over the R Lmax A(L)ω0(L)Qext(L)n(L)dL Lmin azimuth angle φ. hω0(reff )i = (A5) R Lmax Under the approximation of Planck’s function Bν (τ) as a A(L)Qext(L)n(L)dL Lmin piecewise linear function in τ between two consecutive lev-

1810 Finally, libRadtran requires the phase matrix hP (reﬀ )i, els, both integrals can be solved as a function of the expo- R −x −y which is computed according to the following equation for1855 nential integral Ei(x) = −∞ e /y dy. 26 C. Emde et al.: The libRadtran software package

Acknowledgements. Numerous colleagues have contributed with software and comments to the package. We would like to thank K. Stamnes, W. Wiscombe, S.C. Tsay, and K. Jayaweera (disort), F. Evans (polradtran), S. Kato (correlated-k distribution), J.-M. Van- 1860 denberghe, F. Hendrick, and M. V. Roozendael (sdisort), T. Char- lock, Q. Fu, and F. Rose (Fu and Liou code), D. Kratz (AVHRR routines), B. A. Baum, P. Yang, L. Bi, H. Gang, J. Key, B. Rein- hardt, and A. Gonzales (ice cloud optical properties), P. Ricchiazzi (LOWTRAN/SBDART gas absorption), M. Hess (OPAC aerosol 1865 database), W. Wiscombe, C. F. Bohren, and D. Huffman (Mie codes), M. Mishchenko (water reﬂectance matrix), O. Engelsen (implementation of ozone cross sections), the ARTS community and Franz Schreier (line-by-line models), J. Betcke (implementation of King Byrne equation). Thanks to all users for feedback and 1870 contributions, which helped to improve the software over the years. Thanks also to L. Scheck for providing the simulated satellite image shown in Sec. 11.2. Finally we thank two anonymous reviewers and the topical editor K. Gierens for their useful comments. Part of the libRadtran development was funded by ESA (ESASLight projects 1875 AO/1-5433/07/NL/HE, AO/1-6607/10/NL/LvH).